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University  of  California  •  Berkeley 

The  Theodore  P.  Hill  Collection 

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Early  American  Mathematics  Books 


Digitized  by  the  Internet  Arciiive 

in  2008  with  funding  from 

IVIicrosoft  Corporation 


http://www.archtve.org/details/arithmeticalexamOOrobirich 


ROBINSOS'S  MATHEMATICAL   SERIES. 

•      ARITHMETICAL 

EXAMPLES: 

OE, 

TEST      EXERCISES 

FOR  THE   USE   OF 

ADVANCED     CLASSES. 


NEW    YORK: 
IVISON,    PHINNEY,   BLAKEMAN-   &   CO., 

48     &     50     WALKER     STREET. 

CHICAGO: 

S.    C.    GRIGGS    &    COMPANY, 

39    &   41    LAKE    STREET. 


ROB  INSON'S 

1 


m 


The  most  Complete,  most  Practical,  and  most  Scientific  Series  of 
Mathematical  Text-Books  ever  issued  in  this  country. 


Bobinson*s  Progressive  Table  Book,  -  -  -  - 
Hobinson*s  Progressive  Primary  Arithmetic,-  -  -  - 
Kobinson's  Progressive  Intellectual  Arithmetic,  -  -  • 
Kobinson's  Budiments  of  "Written  Arithmetic,  -  -  - 
Bobinson's  Progressive  Practical  Arithmetic,  -  -  - 
Bobinson's  Key  to  Practical  Arithmetic,  -  -  -  -  - 
Bobinson's  Progressive  Higher  Arithmetic,  -  -  -  - 
Bobinson's  Key  to  Higher  Arithmetic,    -       -       •       •       - 

Bobinson's  Arithmetical  Examples,  - 

Bobinson's  New  Elementary  Algebra,     -      -      -      -      - 

Bobinson's  Key  to  Elementary  Algebra,  -      -      -      -      - 

Bobinson's  University  Algebra,  ------- 

Bobinson's  Key  to  University  Algebra,  -      -      -      -      - 

Bobinson's  New  University  Algebra,        -----. 

Bobinson's  Key  to  New  University  Algebra,  -       -      -      - 

Bobinson's  New  Geometry  and  Trigonometry,    -      -      - 
Bobinson's  Siirveying  and  Navigation,     -       -       -       -       - 

Bobinson's  Analyt.  Geometry  and  Conic  Sections, 
Bobinson's  Differen.  and  Int.  Calculus,  (in  prepafation,)- 

Bobinson's  Elementary  Astronomy, 

Bobinson's  University  Astronomy,     -----. 

Bobinson's  Mathematical  Operations, 

Bobinson's  Key  to  Geometry  and  Trigonometry,  Conic 
Sections  and  Analytical  Geometry,      .      -      -      -      - 


Entered,  according  to  Act  of  Congress,  in  the  year  1864,  by 

DANIEL    W.    FISH,    A.M., 

In  the  Clerk's  OflBice  of  the  District  Court  of  the  United  States,  for  the  Northern 
District  of  New  York. 


PREFACE 


In  the  preparation  of  this  work,  it  was  not  designed  to  make 
a  book  to  take  the  place  of  any  other,  nor  one  to  constitute  a 
necessary  part  of  the  series  to  which  it  belongs,  nor  to  adapt 
it  to  the  use  of  beginners,  or  those  commencing  the  study  of 
Arithmetic  ;  but  it  was  pi'tpared  to  meet  a  demand  in  graded 
and  advanced  schools  for  a  larger  number  of  carefully  pre- 
pared and  practical  examples  for  review  and  drill  exercises 
than  are  furnished  from  ordinary  text-books ;  and  it  may  be 
used  in  connection  with  any  other  series  of  Arithmetics. 

Of  course,  it  is  no  substitute  for  a  systematic  treatise.  On 
the  contrary,  its  leading  aim  is  to  bring  together  promis- 
cuously a  large  number  of  practical  examples,  involving  nearly 
^11  the  principles  and  ordinary  processes  of  common  Arith- 
metic,'and  designed  thoroughly  to  test  the  pupil's  judgment ; 
to  bring  into  use  his  knowledge  of  the  theory  and  applications 
of  numbers  ;  to  cultivate  a  habit  of  patient  investigation  and 
self-reliance ;  to  test  the  truth  and  accuracy  of  his  own  pro- 
cesses by  proof — the  only  test  he  will  have  to  depend  upon 
in  all  the  computations  in  real  business  transactions  in  after 
life  ;  in  a  word,  to  make  him  independent  of  the  text-book, 
and  of  written  rules  and  analysis. 

Although  the  examples  are  promiscuous,  yet  there  is  a 
general  classification  of  them,  the  work  bemg  divided  into  six 
chapters.      Tlic    first   chapter    presents   the   Standards   and 


IV  PREFACE. 

Tables  of  Weights  and  Measures ;  the  second  involves  the 
applications  of  the  Simple  Rules  of  Arithmetic;  the  third 
embraces  Common  and  Decimal  Fractions ;  the  fourth  takes 
in  Compound  and  Denominate  Numbers ;  the  fifth  involves 
Percentage,  in  all  its  varied  applications  ;  and  the  sixth  com- 
prehends all  other  subjects  properly  belonging  to  this  science. 
The  examples  in  each  chapter  involve  the  combination  and 
application  of  the  prmciples  and  processes  contained  in  the 
preceding  ones,  but  not  to  any  extent  those  of  the  following 
chapters.  Classes,  therefore,  that,  in  regular  course,  have  gone 
over  the  Simple  Rules  of  Arithmetic  only,  will  find  in  the 
second  chapter  of  this  book  all  they  need  in  the  way  of  sup- 
plementary examples  for  drill  and  review.  Those  who  have 
finished,  in  any  systematic  treatise,  the  study  of  Fractions, 
will  here  have  in  chapter  third  proper  exercises  to  try  their 
skill  in  this  part  of  the  science ;  and  so  they  may  proceed  by 
successive  reviews,  till  the  same  searching  test  comes  to  be 
ai^plied  to  every  part  of  the  subject. 

Two  editions  are  printed  ;  one  with  answers  at  the  close  of 
the  book,  for  the  use  of  teachers,  so  that  when  different  mem- 
bers of  tlie  same  class  obtain  different  results  to  the  same 
example,  he  may  decide  which  is  correct,  without  being 
obliged  to  take  the  time  neco  ary  to  solve  or  verify  it  him- 
self The  other  edition  is  without  answers,  and  designed 
for  the  use  of  classes, 

D.  W.  F. 

New  York,  July,  1864. 


MEi^SXJRES. 


CHAPTER  I. 

1.  Measure  is  that  by  which  extent,  dimension,  capacity, 
or  amount  is  ascertained,  determined  according  to  some  fixed 
standard. 

Note. — The  process  by  -which  the  extent,  dimension,  capacity,  or  amount  is  ascer- 
tained, is  called  Measuring  ;  and  consists  in  comparing  the  thing  to  be  measured  with 
Bome  conventional  standard. 

Measures  are  of  seven  kinds : 

1.  Length.  4.  "Weight,or  Force  of  Gravity. 

2.  Surface  or  Area.  5.  Time. 
'3.  Solidity  or  Capacity.       6.  Angles. 

7.  Money  or  Value. 

The  first  three  kinds  may  be  properly  divided  into  two 
classes — Measures  of  Extension  and  Measures  of  Capacity. 

MEASURES   OF   EXTENSION. 
^     2.  Extension  has  three  dimensions — length,  breadth,  and 
thickness. 

A  Line  has  only  one  dimension  — length. 

A  Surface  or  Area  has  two  dimensions — length  and  breadth. 

I.  Linear  Measure. 

3.  Linear  Measure,  also  called  Long  Measure,  is  used 
in  measuring  lines  or  distances. 


TABLE. 

12  inches  (in.) 

make  1  foot. 

ft. 

8  feet 

u 

1  yard, 

yd. 

5i  yards,  or  16i  feet. 

u 

1  rod. 

rd. 

40  rods 

u 

1  furlong, 

fur. 

8  furlongs,  or  320  rods, 

u 

1  statute  mile. 

mi. 

6 


MEASURES    OF    EXTENSION. 


The  following  denominations  are  also  in  use  : 


3       barleycorns    make    1  inch, 


inches 


1  hand, 


used  by  shoemakers  in 
measuring  the  length  of 
the  foot. 

used  in  measuring  the 
height  of  horses  directly 
over  the  fore-feet. 


9 

it 

1  span. 

21.888    « 

u 

1  sacred  cubit. 

3       feet 

(( 

1  pace. 

6 

(( 

1    fjithom        used  in  measuring  depths 
1  latnom,      ^^^^^^ 

1.15  statute    miles  " 


3      geographic 
60 

69.16  statute 
360       degrees 


or 


used  in  measur- 
1  geographic  mile,  -l  ing  distances  at 
/  sea. 

1  league. 

iof  latitude  on  a  meridian 
or  of   longitude  on    the 
equator. 
the  circumference  of  the  earth. 


Notes.— 1.  For  the  purpose  of  measuring  cloth  and  other  goods  sold  by  the  yard, 
the  yard  is  divided  into  halves,  fourths,  eighths,  and  sixteenths.  The  old  table  of 
Cloth  Measure  is  practically  obsolete. 

2.  A  span  is  the  distance  that  can  be  reached,  spanned,  or  measured  between  the 
end  of  the  middle  finger  and  the  end  of  the  thumb.  Among  sailors  8  spans  are  equal 
to  1  fathom. 

3.  The  geographic  mile  is  ^\j  of  ^^^  or  ^tsoo  of  the  distance  round  the  center  of 
the  earth.     It  is  a  small  fraction  more  thaii  1.15  statute  miles. 

4.  The  cubit  was  originally  the  length  of  a  man's  forearm  and  hand;  or  the  dis- 
tance from  the  elbow  to  the  end  of  the  middle  finger 

5.  The  length  of  a  degree  of  latitude  varies,  being  68.72  miles  at  the  equator,  68.9 
to  69.05  miles  in  middle  latitudes,  and  69.30  to  69.34  miles  in  the  polar  regions.  The 
mean  or  average  length,  as  stated  in  the  table,  is  the  standard  recently  adopted  by 
the  U.  S.  Coast  Survey.  A  degree  of  longitude  is  greatest  at  the  equator,  where  it  is 
69.16  miles,  and  it  gradually  decreases  toward  the  poles,  where  it  is  0. 

surveyor's  linear  MEASURE. 

4.  A  Gunter's  Chain,  used  by  land  surveyors,  is  4  rods, 
or  66  feet  long,  and  consists  of  100  links. 


TABLE. 

7.92  inches  (in.)         make  1  link, 

1. 

25       links                        "      1  rod. 

rd. 

4       rods,  or  66  feet,     "      1  chain. 

ch. 

80       chains                      "      1  mile, 

mi. 

Note. — The  denomination,  rods,  is  seldom  used  in  chain  measure,  distances  being 
taken  in  chains  and  links. 


u 

(( 

yard, 

sq.yd. 

(( 

u 

rod, 

sq.  rd. 

a 

a 

rood, 

R. 

(( 

acre, 

A. 

(( 

cm  ITT 

o  mil/ii 

C^n       TY11 

MEASURES    OF   EXTENSION.  7 

II.  Square  Measure. 

5.  Square  Measure  is  used  in  computing  areas  or  sur- 
faces ;  as  of  land,  boards,  painting,  plastering,  paving,  etc. 

TABLE. 

144    square  inches  (sq.  in.)  make  1  square  foot,    sq.  ft. 
9         "       feet 
?       301       "       yards 
40         "       rods 

4    roods 
640    acres 
Artificers  estimate  their  work  as  follows : 
By  the  square  foot :   glazing  and  stone-cutting. 
By  the  square  yard :  painting,  plastering,  paving,  ceiling, 
and  paper-hanging. 

By  the  square  of  100  square   feet :  flooring,  partitioning, 
roofing,  slating,  and  tiling. 

Bricklaying  is  estimated  by  the  thousand  bricks,  by  the 
square  yard,  and  by  the  square  of  100  square  feet. 

Notes. — ^1.  In  estimating  the    painting  of  moldings,  cornices,  etc.,  the  measuring- 
line  is  carried  into  all  the  moldings  and  cornices. 

2.  In  estimating  brick-laying  by  either  the  square  yard  or  the  square  of  100  feet, 
the  work  is  understood  to  be  12  inches  or  1^  bricks  thick. 
^      3.  A  thousand  shingles  are  estimated  to  cover  1  square,  being  laid  5  inches  to  the 
weather. 

surveyors'  square  measure. 

6.  This  measure  is  used  by  surveyors  in  computing  the 
area  or  contents  of  land. 

table. 
625  square  links  (sq.  1.)  make  1  pole,  P. 

16  poles  "       1  square  chain,  sq.  ch. 

10  square  chains  "      1  acre,  A. 

640  acres  "       1  square  mile,  sq.  mi. 

36  square  miles  (6  miles  square)   "       1  township,  Tp. 

Notes. — 1.  A  square  mile  of  land  is  also  called  a  section. 

2.  Canal  and  railroad  engineers  commonly  use  an  engineers*  chain,  which  consists 
of  100  links,  each  1  foot  long. 

3.  The  contents  of  land  are  commonly  estimated  in  square  miles,  acres,' and  hun- 
dredths ;  the  denomination,  rood^  is  rapidly  going  into  disuse. 


8  MEASURES   OF   EXTENSION. 

III.  Cubic  Measure. 
7.  Cubic  Measure,  also  called  Solid  Measure,  is  used  in 
computing  the  contents  of  solids,  or  bodies ;  as  timber,  wood, 
stone,  etc. 

TABLE. 

1728  cubic  inches  (cu.  in.)             make  1  cubic  foot,     cu.  fl. 

27  cubic  feet                                    "     1  cubic  yard,  cu.  yd. 

40  cubic  feet  of  round  timber,  or  )   ,,     ,  ,           ,     ^         ^ 

50  "        "     hewn      "           [        ^  *°"  °'- '°^'''       T. 

16  cubic  feet                                    "     1  cord  foot,      cd.  ft. 

8    cord  feet,  ov  )  ..     _        i    ^         •,    m 

,00        X.-  -4-   4.       (  1  cord  of  wood,  Cd. 

128    cubic  feet       ) 

24|  cubic  feet  "     1  j  11"— y"!'  \^'^- 

Notes.— 1.  A  cubic  yard  of  earth  is  called  a  load. 

2.  Railroad  and  transportation  companies  estimate  light  freight  by  the  space  it 
occupies  in  cubic  feet,  and  heavy  freight  by  weight. 

3.  A  pile  of  wood  8  feet  long,  4  feet  wide,  and  4  feet  high,  contains  1  cord  ;  and  a 
cord  foot  is  1  foot  in  length  of  such  a  pile. 

4.  A  perch  of  stone  or  of  masonry  is  16^  feet  long,  H  feet  wide,  and  1  foot  high. 

5.  Joiners,  bricklayers,  and  masons,  make  an  allowance  for  windows,  doors,  etc., 
of  one  half  the  openings  or  vacant  spaces.  Bricklayers  and  masons,  in  estimating 
their  work  by  cubic  measure,  make  no  allowance  for  the  corners  of  the  walls  of 
houses,  cellars,  etc.,  but  estimate  their  work  by  the  girt,  that  is,  the  entire  length  of 
the  wall  on  the  outside. 

6.  Engineers,  in  making  estimates  for  excavations  and  embankments,  take  the 
dimensions  with  a  line  or  measure  divided  into  feet  and  decimals  of  a  foot.  The 
computations  are  made  in  feet  and  decimals,  and  the  results  are  reduced  to  cubic 
yards.  In  civil  engineering,  tlie  cubic  yard  is  the  unit  to  which  estimates  for  exca- 
vations and  embankments  are  finally  reduced. 

7.  In  scaling  or  measuring  timber  for  shipping  or  freighting,  |  of  the  solid  contents 
of  round  timber  is  deducted  for  waste  in  hewing  or  sawing.  Thus,  a  log  that  will 
make  40  feet  of  hewn  or  sawed  timber,  actually  contains  50  cubic  feet  by  measure- 
ment ;  but  its  market  value  is  only  equal  to  40  cubic  feet  of  hewn  or  sawed  timber. 
Hence,  ihe  cubic  contents  of  40  feet  of  round  and  50  feet  of  hewn  timber,  as  esti- 
mated for  market,  are  identical. 

8.  Sawed  timber,  joists,  plank,  and  scantlings  are  generally  bought  and  sold  by 
what  is  called  board  measure. 

9.  A  cubic  foot  of  water  at  the  maximum  density,  at  the  level  of  the  sea,  weighs 
62J;  pounds,  avoirdupoLs. 

10.  A  cubic  foot  of  lead  weighs  708.J  lbs.  ;  of  brass,  634}  lbs.  ;  of  copper,  555  lbs.  ; 
of  wrought  iron,  4S6}  lbs.  ;  of  cast-iron,  4.50>  lbs. ;  of  ninrblo,  171  lbs.;  of  granite,  165 
lbs. ;  of  clay,  130  lbs. ;  of  common  soil,  124  lbs. ;  of  bricks,  l'?4  lbs. ;  of  sand,  05  lbs. ; 
of  sea  water,  64/77  lbs. ;  of  oak  wood,  55  lbs.  ;  of  Anthracitp  roal,  54  lbs.  ;  of  Bitumi- 
nous coal,  50  lbs.  ;  of  red  pine  wood,  42  lbs.  ;  and  of  white  pine  wood,  30  lbs. 


MEASUKES    OF   CAPACITY.  9 

MEASURES  OF  CAPACITY. 

I.  Liquid  Measure. 
8.  Liquid  Measure,  also  called  Wine  Measure,  is  used 
in  measuring  liquids  ;  as  liquors,  molasses,  water,  etc. 


TABLE. 

4    gills 

make  1  pint. 

pt. 

2    pints 

"     1  quart, 

qt. 

4    quarts 

"     1  gallon. 

gal. 

31*  gallons 

"     1  barrel, 

bbl. 

2    barrels, 

or  63 

gal. 

"     1  hogshead, 

hhd. 

Notes.— 1.  The  denominations,  barrel  and  hogshead,  are  used  in  estimating  the 
capacity  of  cisterns,  reservoirs,  vats,  etc.  In  Massachusetts  the  barrel  is  estimated 
at  32  gallons,  in  some  States  3U  gallons,  and  in  others  from  28  to  32  make  1  barrel. 

2.  The  tierce,  hogshead,  pipe,  butt,  and  tun  are  the  names  of  casks,  and  do  not  ex- 
press any  fixed  or  definite  measures.  They  are  usually  gauged,  and  have  their 
capacities  in  gallons  marked  on  them.  Several  of  these  denominations  are  still  in 
use  in  England. 

The  following  denominations  are  also  in  use  : 
9    old  ale  gallons  make  1  firkin. 


4    firkins 

7A  Imperial  gallons 
52i  Imperial  gallons,  or  ) 
■    63    wine             "              \ 

"     1  barrel  of  beer. 
"     1  firkin. 

"     1  hogshead. 

70    Imperial       "        or  ) 

84    wine             "             ') 

2    hogsheads,  that  is       ) 

"     1  puncheon  or 
"     i  of  a  tun. 

105    Imperial  gallons  or  > 
126    wine             "              ) 

"     1  pipe. 

2    pipes 

"     1  tun. 

Pipes  of  wine  are  of  different  ( 
110  wine  gallons  make 

120       "          "            « 

capacities,  as  follows : 
1    pipe  of  Madeira. 

( Barcelona, 
1       "        -{  Vidonia,  or 

130       "          "            " 
138       "          "            " 

1 
1 

(  Teneriflie. 
Sherry. 
Port. 

140      "          '.'•            *? 

1 

"    ^,        {  Bucellas,  or 
)  Lisbon. 

10  MEASURES    OF    CAPACITY. 

BEER    MEASURE. 

9.  Beer  Measure  is  a  species  of  liquid  measure  used  in 
measuring  beer,  ale,  and  milk. 

TABLE. 

2    pints  (pt.)                       make  1  quart,  qt. 

4    quarts                                "       1  gallon,  gal. 

36    gallons                              «       1  barrel^  bbl 

IJ  barrels,  or  54  gallons,      "      1  hogshead,  hhd. 

This  measure  is  not  a  standard ;  it  is  rapidly  falling  into 

disuse. 

II.  Dry  Measure. 

10.  Dry  Measure   is  used  in  measuring  articles,  not 
liquid ;  as  grain,  fruit,  salt,  roots,  ashes,  etc. 

table. 

2  pints  (pt.)    make  1  quart,  qt. 

8  quarts  "       1  peck,  pk. 

4  pecks  "       1  bushel,  bu.  or  bush. 

The  following  are  sometimes  used  : 

8  bushels  of  70  pounds  each  make  1  quarter  of  wheat. 
86         "     heaped  measure,         "      1  chaldron  of  coal. 

Note. — The  quarter  of  wheat  is  560  pounds,  or  ^  of  a  ton  of  2240  pounds. 

11.  Comparative  Table  of  Measures  of  Capacity. 

Cubic  in.  in      Cubic  in.  in      Cubic  in.  in      Cubic  in.  in 
one  gallon.        one  quart.         one  pint.  one  gill. 

Wine  measure, 231  57|  28|  T/^ 

Dry  measure  (A  pk.),  268|  67i  33f  8| 

Notes. — 1.  The  beer  gallon  of  282  inches  is  retained  in  use  only  by  custom. 

2.  Grain  and  some  other  commodities  are  sold  by  stncken  measure,  and  in  such 
cases  the  "  measure  is  to  be  stricken  with  a  round  stick  or  roller,  straight,  and  of  the 
same  diameter  from  end  to  end." 

3.  Coal,  ashes,  marl,  manure,  corn  in  the  ear,  fruit,  and  roots  are  sold  by  heap 
measure.  The  bushel,  heap  measure,  is  the  Winchester  bushel  heaped  in  the  form 
of  a  cone,  which  cone  must  be  19^^  inches  in  diameter  (=  to  the  outside  diameter  of 
the  standard  bushel  measure),  and  at  least  six  inches  high.  A  bushel,  heap  mea- 
sure, contains  274T.71 67  cubic  inches,  or  597.296T  cubic  inches  more  than  a  bushel 
stricken  measure.  Since  1  peck  contains  ^"'"'*  =  537.005  cubic  inches,  the  bushel, 
heap  measure,  contains  59.0917  cubic  inches  more  than  5  pecks.  As  this  is  about  1 
bu.  1  pk.  If  pt.,  it  is  sufficiently  accurate  in  practice,  to  call  5  pecks  stricken  measure 
a  heap  bushel. 

4.  A  standard  bushel,  stricken  measure,  is  commonly  estimated  at  2150.4  cubic  in- 
ches. The  old  English  standard  bushel  from  which  the  United  States  standard  bushel 
was  derived,  was  kept  at  "Winchester,  England;  hence  the  name. 


WEIGHTS.  11 

WEIGHTS. 
I.  Troy  Weight. 

12.  Troy  Weight  is  used  iu  weighing  gold,  silver,  and 
jewels. 

TABLE.  ! 

24  grains  (gr.)     make  1  pennyweight,  pwt.  or  dwt. 
20  pennyweights     "      1  ounce,  oz. 

12  ounces  "      1  pound,  lb. 

Note.— Troy  weight  is  sometimes  called  Goldsmith's  Weight. 

II.  Avoirdupois  Weight. 

13.  Avoirdupois  Weight  is  used  for  all  the  ordmary 
purposes  of  weighing. 

TABLE. 

16  drams  (dr.)  make  1  ounce,  oz. 

16  ounces  "      1  pound,  lb. 

100  lb.  "      1  hundred  weight,  cwt. 

20  cwt.,  or  2000  lbs.,     "       1  ton,  T. 

Note. — The  long  or  gross  ton,  hundred  weight,  and  quarter  were  formerly  in  com- 
mon use  ;  but  they  are  now  seldom  used  except  in  estimating  English  goods  at  the 
United  States  Custom-houses,  in  freighting  and  wholesaling  coal  from  the  Pemisyl- 
vania  mines,  and  in  the  wholesale  iron  and  plaster  trade. 

LONG    TON    TABLE. 

28  lb.  make  1  quarter,  marked    qr. 

4  qr.     =    112  1b.     "      1  hundredweight,       "       cwt. 
20  cwt.  =  2240  lb.    "      1  ton,  "         T. 

The  following  denominations  are  also  in  use  : 
8  pounds  of  butchers'  meat         make  1  stone. 
14  "         other  commodities      "     1     "     or  |  of  a  cwt. 

2  stone,  or  28  pounds  "     1  todd  of  wool. 

70  pounds  of  salt  "     1  bushel.  - 

make  1  firkin  of  butter. 
"       1  quintal  of  dried  salt  fish. 
"      1  cask  of  raisins. 
"      1  barrel  of  flour. 
"      1      "       "  beef,  pork,  or  fish. 
"      1      "       "  salt  at  the  N.Y.  State  salt-works. 


56 

(( 

100 

<c 

100 

(( 

196 

u 

200 

(( 

280 

a 

12 


WEIGHTS. 


NOTKS.— The  English  quarter  is  2S  pounds,  the  hundred  weight  is  112  pounds,  and 
the  ton  is  20  hundred  weight,  or  2240  pounds. 

2.  The  weight  of  a  barrel  of  flour  is  7  quarters  of  old,  or  long  ton  weight 

3.  The  weight  of  a  bushel  of  Indian  corn  and  rye,  as  adopted  by  most  of  the 
States,  and  of  a  busliel  of  salt  is  2  quarters ;  and  of  a  barrel  of  salt  10  quarters,  or 
i  of  a  long  ton. 

4.  The  terms  gross  and  net  are  used  in  this  weight.  Gross  tveight  is  the  weight  of 
the  goods,  together  with  the  box,  cask,  or  whatever  contains  them.  Net  weight  is 
the  weight  of  the  goods  alone. 

14.  The  weiglit  of  the  bushel  of  certain  grains  and  roots 
has  been  fixed  by  statute  in  many  of  the  States ;  and  these 
statute  weights  must  govern  in  buying  and  selling,  unless 
specific  agreements  to  the  contrary  be  made. 

TABLE    OF    AVOIRDUPOIS    POUNDS    IN    A    BUSHEL, 

As  prescribed  hy  statute  in  the  several  States  named. 


Commodities. 


Barley 

Beans 

Blue  Grass  Seed.. 

Buckwheat 

Castor  Beans 

Clover  Seed 

Dried  Apples 

Dried  Peaches 

Flax  Seed  

Hair 

Hemp  Seed 

Indian  Corn 

Indian  Corn  in  ear. 
India:!  Corn  Meal. 

Mineral  Coal' 

Oats , 

Onions 

Peas , 


Potatoes 

Rye 

Rye  Meal 

Saltt 

Timothy  Seed. 

Wheat 

Wheat  Bran.. 


52  56 


5G 


50 

m 

5757 

60 1 60 
56^56 

50  50 
45;45 
60,60 
20 '20 


60 


<s    9  ■  »- 


I  o 


..  ,l|.si.„ 


60  60 


48  48 
160 

ll4 
42  52 

|46 
60  60 
28 1 24 
28  33 

j56 

'44 
56  52 

I 


60  60 

"I 

50 

45! 
60 1 

I20' 


48'4S:4S 
02 


561 
441 
60  60 


56 


56 


60 


43 


56 


36  32 

501 


6OCOI6O 
56  56  56 


|46 
60:60 


*  In  Kentucky  80  lbs.  of  bituminous  coal,  or  70  lbs.  of  cannel  coal,  make  1  bushel. 
t  In  Pennsylvania  80  lbs.  coarse,  70  lbs.  ground,  or  62  lbs.  fine  salt  make  1  bushel ; 
and  in  Illinois,  50  lbs.  common  or  55  lbs.  fine  salt  make  1  bushel. 
%  In  Maine  01  lbs.  of  ruta  baga  turnips  or  beets  make  1  bushel. 


WEIGHTS.  .13 


III.  Apothecaries'  Weight. 

15.  Apothecaries'  Weight  is  used  by  apothecaries  and 
physicians  in  compounding  medicines ;  but  medicines  are 
bought  and  sold  by  avoirdupois  weight. 

TABLE. 

20  grains  (gr.)  make  1  scruple,  sc.  or  3. 

3  scruples  "      1  dram,  dr.  or  3. 

8  drams  "      1  ounce,  oz.  or  |. 

12  ounces  "      1  pound,  lb.  or  ft. 

apothecaries'  fluid  measure. 

16.  The  measures  for  fluids,  as  adopted  by  apothecaries  and 
physicians  in  the  United  States,  to  be  used  in  compounding 
medicines,  and  putting  them  up  for  market,  are  given  in  the 
following 

TABLE. 

60  minims  (ni)  make  1  fluidrachm,  f3. 

8  fluidrachms      "      1  fluidounce,  ff . 

16  fluidounces       "      1  pint,  O. 

8  pints                 "      1  gallon,  Cong. 

17.  comparative  table  of  weights. 

Troy.  Avoirdupois.  Apothecaries'. 

1  pound  =  5760  grains,  =  7000  grains.    =  5760  grains, 
1  ounce  =    480       "      =    437.5     "      =    480      " 

175  pounds,  =    144  pounds,  =    175  pounds, 

18.    COMPARATIVE    TABLE. 

United  States.  English.  French. 

Extension,    Yd.  of  3  ft.,  or  36  in.  Same  as  tJ.  S.  Metre,  30.36F5  in. 

j  Wine  gal.,  231  cu.  in.  Imp'l  gal.,  277-274  cu.  in.  Litre,  61.53:94  cu.  in. 

Capacity,    ^  ^j^^^j^,^  ^^^  2150-42  cu-  in-  Imp'l  bu.,  2218.192  cu.in. 

Weight,         Troy  lb.,  5760  gr.  Imperial  lb.,  5760  gr.  Grammel5.433159T.gr. 

Notts.— An  Imperial  gallon  is  equal  to  1.2  wine  gallons. 

2.  An  old  ale  or  beer  gallon  is  very  nearly  equal  to  1.221  wine  gallons,  or  1.01 4 
Imperial  gallons. 


14 


MEASURES   OF   TIME   AND   ANGLES. 


MEASURES  OF  TIME  AND  ANGLES. 


19.  Time  is  the  measure  of  duration. 


TABLE. 

60  seconds   (sec.)  make  1  minute, 

min. 

60  minutes 

"       1  hour, 

h. 

24  hours 

"      1  day. 

da. 

7  days 

"      1  week. 

wk. 

365  days 

"      1  common  year, 

.  yr. 

366  days 

"      1  leap  year, 

y^' 

12  calendar  months  "      1  year, 

yr. 

100  years 

"      1  century. 

c. 

The  calendar  year  is 

divided  as  follows 

;: 

No.  of  month.    Season. 

Names  of  months.      Abreviations. 

No.  of  days. 

^  I      Winter 

J  January, 
(  February, 

Jan. 

31 

^      r                  T  T    llXv\^A  • 

Feb. 

28  or  29 

3 

I  March, 

Mar. 

31 

4  [•      Spring, 

\  April, 

Apr. 

30 

5) 

(May, 

31 

6 

(  June, 

Jun. 

30 

7  >-      Summer, 

\  July, 

31 

8 

(  August, 

Aug. 

31 

^) 

{  September, 

Sept. 

30 

10  V      Autumn, 

•|  October, 

Oct. 

31 

11  ) 

(  November, 

Nov. 

30 

12         Winter, 

December, 

Dec. 

31 

Note. — ^In  most  business  transactions  30  days  are  called  1  month. 
MEASURE    OF    ANGLES. 

20.  Circular  Measure,  or  Circular  Motion,  is  used  prin- 
cipally in  surveying,  navigation,  astronomy,  and  geography, 
for  reckoning  latitude  and  longitude,  determining  locations  of 
places  and  vessels,  and  computing  difference  of  time. 

Every  circle,  great  or  small,  is  divisible  into  the  same 
number  of  equal  parts  :  as  quarters,  called  quadrants  ;  twelfths, 
called  signs  ;  360 ths,  called  degrees,  etc. 

TABLE. 

60  seconds  (")       make  1  minute,    '. 


60  minutes 
30  degrees 
12  signs,  or  360", 


1  degree,  ^ 
1  sign,  S. 
1  circle,     C. 


MISCELLANEOUS   MEASURES. 


15 


Notes. — 1.  Minutes  of  the  earth's  circumference  are  called  geographic  or  nautical 
miles. 

2.  A  Knot  is  a  nautical  or  geographical  mile.     Thus,  the  expression,  "  ten  knots  an 
hour,"  denotes  ten  geographical  miles  per  hour. 

3.  One  English  mile  equals  5280  feet,  and  one  nautical  or  geographical  mile  equals 
6086  feet. 

4.  The  denomination,  signs,  is  confined  exclusively  to  Astronomy. 

5.  A  degree  has  no  fixed  linear  extent.    When  applied  to  any  circle  it  is  always 
»ao  P^rt  of  the  circumference.    But,  strictly  speaking,  it  is  not  any  pact  of  a  circle. 

6.  90°  make  a  quadrant  or  right  angle  ; 
60°      "    a  sextant  or  I  of  a  circle. 


MISCELLANEOUS    TABLES. 


21.    COUNTING. 

12  units  or  things  make  1  dozen. 


12  dozen 
12  gross 
20  units 

24  sheets 
20  quires 
2  reams 
5  bundles 


"  1  gross. 

"  1  great  gross. 

"  1  score. 

22.    PAPER. 

make  1  quire. 

"  1  ream. 

"  1  bundle. 

"  1  bale. 


23.    BOOKS. 


The  terms  foliOj  quarto,  octavo,  duodecimo,  etc.,  indicate  the 
number  of  leaves  into  which  a  sheet  of  paper  is  folded. 
A  sheet  folded  in    2  leaves  is  called  a  folio. 


A  sheet  folded  in  4  leaves 
A  sheet  folded  in  8  leaves 
A  sheet  folded  in  12  leaves 
A  sheet  folded  in  16  leaves 
A  sheet  folded  in  18  leaves 
A  sheet  folded  in  24  leaves 
A  sheet  folded  in  32  leaves 


a  quarto,  or  4to. 

an  octavo,  or  8vo. 

a  12mo. 

a  16mo. 

an  18mo. 

a  24mo. 

a  32  mo. 


24.    COPYING. 

72  words  make  1  folio,  or  sheet  of  common  law. 


90 


1 


"   chancery. 


16  MONEY   AND   CURRENCIES. 

MONEY  AND   CURRENCIES. 
I.  United  States  Money. 

25.  The  currency  of  the  United  States  is  decimal  currency, 
and  is  sometimes  called  Federal  Money, 

TABLE. 

10  mills  (m.)  make  1  cent,  ct, 

10  cents               "     1  dime,  d. 

10  dimes             "     l  dollar,  %. 

10  dollars            "     1  eagle,  E. 

Coins.— The  gold  coins  are  the  double  eagle,  eagle,  half  eagle,  quarter  eagle,  three 
dollar  piece,  and  dollar. 

The  silver  coins  are  the  half  and  quarter  dollar,  dime  and  half  dime,  and  three 
cent  piece. 

The  nickel  coin  is  the  cent. 

STATE    CURRENCIES. 

26.  United  States  money  is  reckoned  in  dollars,  dimes, 
cents,  and  mills,  one  dollar  being  uniformly  valued  in  all 
the  States  at  100  cents ;  but  in  many  of  the  States  money  is 
sometimes  reckoned  in  dollars,  shillings,  and  pence. 

Georgia  Currency/. 
Georgia,  South  Carolina,  |l=4s.  8d.=56d. 

Canada  Currency. 
Canada,  Nova  Scotia,  |l=5s.=::60d. 

New  England  Currency. 

New  England  States,  Indiana,  Illinois,  \ 

Missouri,  Virginia,  Kentucky,  Ten-  V  $l=r6s.=72d. 
nessee,  Mississippi,  Texas,  ) 

Pennsylvania  Currency. 
New  Jersey,  Pennsylvania,  Delaware,  )  gi_o'g  qa  — QOd 
Maryland,  ) 

New  York  Currency. 
New  York,  Ohio',    Michigan,  North)  ^,_j.    —Ckr\ 
Carolina.  i 


MONEY    AND    CUEKENCIES.  17 


II.  Canada  Money. 

27.  The  currency  of  the  Canadian  provinces  is  decimal,  and 
the  table  and  denominations  are  the  same  as  those  of  the 
United  States  money. 

Note.— The  decimal  currency  was  adopted  by  the  Canadian  Parliament  in  1858, 
and  the  Act  took  efifect  in  1859.  Previous  to  the  latter  year  the  money  of  Canada  was 
reckoned  in  pounds,  shillings,  and  pence,  the  same  as  in  England. 

Coins. — The  silver  coins  are  the  shilling,  or  20-cent  piece, 
the  dime,  and  half  dime. 
The  copper  coin  is  the  cent. 

Notes.— The  20-cent  piece  represents  the  value  of  the  shilling  of  the  old  Canada 
currency. 

2.  The  value  of  the  20-cent  piece  in  United  States  money  is  18|  cents,  of  the  dime 
9i  cents,  and  of  the  half  dime  4|  cents. 

3.  Every  3d.  of  the  old  coinage  is  equal  to  5  cents  of  the  new. 

III.  English  Money. 

28.  English  or  Sterling  Money  is  the  currency  of  Great 
Britain. 

TABLE. 

4  farthings  (far.  or  qr.)  make  1  penny,  d. 

12  pence  "     1  shilling,  s. 

20  shillings  "     1  pound  or  sovereign,  £  or  sov. 

Notes. — 1.  Farthings  are  generally  expressed  as  fractions  of  a  penny;  thus,  1  far., 
sometimes  called  1  quarter,  (qr.)  =  :^d.  ;  3  far.  =  fd. 

2.  The  gold  coins  are  the  sovereign  (=  £1)  and  the  half  sovereign  (=  10s.) 

8.  The  silver  coins  are  the  crown  (=  5s.),  the  half  crown  (=  2s.  6d.),  the  shilling, 
and  the  6  penny  piece. 

4.  The  copper  coins  are  the  penny,  half  penny,  and  farthing. 

5.  The  guinea  (=  21s.)  and  the  half  guinea  (=  10s.  6d.  sterling)  are  old  gold  coins, 
that  are  still  in  circulation,  but  are  no  longer  coined. 

6.  In  France  accounts  are  kept  in  francs  and  decimes.  A  franc  is  equal  to  18.6 
cents  United  States  money. 

7.  The  pound  {£)  is  not  a  coin,  but  stands  for  20s. ;  it  is  represented  by  the  sove- 
reign, or  the  bank  note  of  £\.  The  pound  is  so  called,  because  its  equivalent,  240d. 
or  '.iUs.,  formerly  contained  a  pound  weight  of  siver,  the  pound  then  being  smaller 
than  at  present.  A  pound  of  standard  silver  is  now  coined  into  66s.  The  value  of 
£1  in  Canada  and  the  United  States  is  $4.84.  Hence  the  value  of  an  English  shilling 
is  241  cents. 


18 


INTEREST. 


INTEREST. 
29.  Legal  Interest  is  the  rate  per  cent,  established  by 
law.     It  varies  in  different  States,  as  follows : 


Alabama, 

8 

per 

cent. 

Minnesota, 

7  per 

cent 

Arkansas, 

6 

a 

u 

Mississippi, 

8 

(( 

(( 

California, 

10 

a 

u 

Missouri, 

6 

u 

(( 

Connecticut, 

6 

u 

u 

New  Hampshire, 

6 

u 

« 

Delaware, 

6 

u 

(( 

New  Jersey, 

6 

u 

(( 

Dist.  of  Columbia 

,6 

u 

u 

New  York, 

7 

u 

u 

Florida^ 

8 

u 

u 

North  Carolina, 

6 

u 

(( 

Georgia, 

7 

(C 

u 

Ohio, 

6 

u 

a 

Illinois, 

6 

(( 

(( 

Pennsylvania, 

6 

u 

(( 

Indiana, 

6 

a 

u 

Rhode  Island, 

6 

u 

a 

Iowa, 

6 

u 

u 

South  Carolina, 

7 

u 

a 

Kentucky, 

6 

u 

a 

Tennessee, 

6 

(( 

u 

Louisiana, 

5 

u 

u 

Texas, 

8 

u 

u 

Maine, 

6 

(( 

u 

U.  States  (debts) 

,6 

(( 

(( 

Maryland, 

6 

u 

u 

Vermont, 

6 

a 

u 

Massachusetts, 

6 

u 

u 

Virginia, 

6 

u 

(( 

Michigan, 

7 

u 

(( 

Wisconsin, ' 

7 

a 

a 

Notes.— 1.  The  legal  rate  in  Canada,  Nova  Scotia,  and  Ireland  is  €-^peT  cent.,  and 
in  England  and  France  5  per  cent. 

2.  When  the  rate  per  cent,  is  not  specified  in  accounts,  notes,  mortgages,  contracts, 
etc.,  the  legal  rate  is  always  understood. 

TABLE. 

30.  Showing  the  number  of  days  from  any  day  of  one  month 
to  the  same  day  of  any  other  month  within  one  year. 


FEOM   ANY 
DAY  OF 


January  .. 
February., 

March 

April 

May , 

June 

July 

August . . . 
September 
October  . . 
November.. 
December . . 


TO  TUE   SAME  DAY   OF 

THE   NEXT 

Jan. 
365 

Feb. 

Mar. 

Apr. 
90 

May. 
120 

June 
151 

July. 
181 

Aug. 
212 

Sept. 
243 

Oct. 

273 

Nov. 
304 

31 

59 

334 

305 

28 

59 

89 

120 

150 

181 

212 

242 

273 

306 

337 

365 

31 

61 

92 

122 

153 

184 

214 

245 

275 

306 

335 

365 

30 

61 

91 

122 

153 

183 

214 

245 

276 

304 

335 

365 

31 

61 

92 

123 

153 

184 

214 

'.'45 

273 

304 

334 

365 

30 

61 

92 

122 

153 

184 

215 

243 

274 

304 

335 

365 

31 

62 

92 

123 

15.". 

1S4 

212 

243 

273 

304 

834 

865 

31 

61 

92 

122 

153 

181 

212 

242 

273 

303 

334 

365 

SO 

61 

92 

123 

151 

182 

212 

243 

273 

304 

333 

365 

31 

61 

.92 

120 

151 

181 

212 

242 

273 

304 

334 

365 

81 

62 

90 

121 

151 

182 

212 

243 

274 

304 

335 

334 

303 

275 

244 

214 

183 

153 

122 

91 

61 

30 

365 


ARITHMETICAL  EXAMPLES, 


CHAPTER   II. 

1.  The  total  length  of  railroads  in  Massachusetts,  Jan.  1st, 
y  1864,  was  1941  miles,  and  the  total  cost  of  the  roads  and 

equipments  up  to  the  same  date,  was    $66809802.      How 
much  had  been  expended  per  mile  1 

2.  At  the  same  date  there  were  112  miles  of  horse-rail- 
roads, costing  for  building  and  equipments  $3979596.  How 
much  more  had  been  expended  per  mile  upon  horse-railroads 
than  upon  steam  railroads  ? 

3.  A  man  bequeathed  his  estate  as  follows:  to  each  of 
his  three  sons,  $8500 ;  to  each  of  his  four  daughters,  $4250  ; 
to  his  wife,  $350  more  than  the  sum  of  the  shares  of  one  son 
and  three  daughters;  and  the  remainder,  which  was  $2000 
more  than  he  gave  to  all  his  family,  he  left  to  benevolent  in- 
stitutions.    What  was  the  value  of  his  estate  1 

4.  The  national  debt  of  Great  Britain  in  1861  was  $133.55 
for  each  person,  and  tlie  population  was  29334788.  What 
was  the  national  debt  1 

5.  At  the  same  date,  the  annual  interest  of  the  national 
debt  was  $127665701.  Required,  the  annual  interest  to  each 
person. 

6.  The  Finances  of  the  State  of  Maine  for  the  year  1 862 
were  stated  as  follows: 


20  ARITHMETICAL   EXAMPLES. 

Receipts. — Balance  in  Treasury,  Jan.  1,  1862,  $68434.63  ; 
receipts  from  Taxes,  $439150,64 ;  receipts  from  Loans  and 
miscellaneous  sources,  1220661.39.  Expenditures. — For  war 
purposes,  1124088.36;  for  soldiers'  allotments,  $109072.31  ; 
for  civil  services,  $400732.45.  Required  the  balance  in 
Treasury,  Jan.  1,  1863. 

7.  The  area  of  Ireland  is  32481  square  miles,  and  5023984 
acres  are  uncultivated.     How  many  more  acres  are  cultivated  ' 
than  3  times  the  number  uncultivated,  there  being  640  acres 
in  one  square  mile  1 

8.  In  1861  England  paid  the  United  States  $132741160 
for  cotton ;  Egypt,  $6225330 ;  and  India,  $31 165565.  In  1863 
she  paid  the  United  States  $2302290 ;  Egypt,  $32996165,  and 
India,  $110258560.  How  much  less  was  paid  for  cotton  by 
England  in  1863  than  in  1861? 

9.  Western  Virginia  embraces  51  counties,  in  which  there 
were,  Oct.  1,  1863,  368623  whites,  3981  free  colored  persons, 
and  20606  slaves.  What  was  the  average  population  in 
each  county  1 

10.  During  the  six  months  ending  March  1, 1864, 1020000 
quarters  of  wheat  were  exported  from  the  United  States. 
How  many  vessels,  each  carrying  600  short  tons,  were  re- 
quired to  ship  the  same  1 

11.  The  city  of  New  York  paid  taxes'  from  1858  to  1864 
amounting  in  the  aggregate  to  $64445967.34.  The  proper- 
ty upon  which  these  taxes  were  assessed  amounted  to 
$531194290  in  1858,  and  $594196863  in  1863.  How  much 
less  than  the  taxes  was  the  increase  of  property  1 

32.  The  number  of  pupils  in  Girard  College  in  1857  was 
295,  and  the  expenses  for  the  year  were  $88173  ;  in  1862  the 
pupils  nil  inhered  400,  and  the  expenses  that  year  were 
$73247.  How  much  less  was  the  expense  per  pupil  in  1862 
than  in  1857? 

13.  Tliere  were  in    operation,  Jan.   1,   1862,  in   the    Nev/ 


ARITHMETICAL    EXAMPLES.  21 

England  States  3641  miles  of  railroad  ;  in  New  York,  2769 ; 
in  Pennsylvania,  2918  ;  in  Virginia,  1729  ;  in  Georgia,  1419 ; 
in  Tennessee,  1253;  in  Ohio,  4232;  in  Indiana,  2169 ;  and 
in  Illinois,  3041.  What  was  the  aggregate  number  of  miles 
in  operation  in  all  these  States  ? 

14.  The  total  length  of  railroad  in  operation  in  the  United 
States,  Jan.  1,  1862,  being  33222  miles,  what  was  the  aggre- 
gate number  of  miles  in  all  the  other  States  not  mentioned  in 
the  preceding  Example  1 

15.  The  total  cost  of  the  Atlantic  Telegraph  Cable,  as 
originally  made,  was  $1258250,  of  which  10  miles  deep-sea 
cable  was  made  at  a  cost  of  $1450  per  mile,  and  25  miles 
shore-ends  at  $1250  per  mile;  the  cost  of  the  remainder  was 
8485  per  mile.     How  many  miles  of  cable  were  made  1 

16.  If  a  house  is  worth  82500,  and  the  farm  on  which  it 
stands,  3  times  as  much,  lacking  $500,  and  the  stock,  one 
half  as  much  as  the  house  and  farm,  what  is  the  value  of  the 
whole  1 

17.  The  population  of  Boston  in  1862  was  177812;  of 
New  York,  805651 ;  of  Philadelphia,  562529;  of  Baltimore, 
212418;  of  New  Orleans,  168675;  of  St.  Louis,  160773;  of 
Cincinnati,  161044,  and  of.  Chicago,  109260.  What  was  the 
entire  population  of  these  cities  1 

18.  The  product  of  three  numbers  is  535500  ;  one  of  the 
numbers  is  68,  and  another  75.     What  is  the  third  ? 

19.  Forty  Michigan  regiments,  whose  original  strength 
was  35630  men,  lost  in  1861-'62,  771  men  in  battle,  1810  by 
disease,  370  missing,  and  3791  were  discharged.  What  was 
the  total  loss  in  two  years,  and,  making  no  allowance  for  re- 
cruits, what  was  the  entire  strength  of  those  regiments,  Jan. 
1,  1863? 

20.  The  population  of  the  New  England  States  in  1860 
was  as  follows  -.—Maine,  628279  ;  New  Hampshire,  326073  ; 
Vermont,  315098;  Massachusetts,  1231066;  Rhode  Island, 


22  ARITHMETICAL   EXAMPLES. 

174620 ;  Connecticut,  460147.     Required  the  entire  popula- 
tion. 

21.  The  Pennsylvania  Central  Railway  is  356  miles  long, 
and  cost  $31450000 ;  the  New  York  Central  Railway  is  655 
miles  long,  and  cost  $38825000 ;  the  Illinois  Central  is  708 
miles  long,  and  cost  $31280000,  and  the  Michigan  Central  is 
329  miles  long  and  cost  $14000000.  Required  the  aggregate 
length  and  cost  of  these  four  roads. 

22.  Of  libraries  containing  10000  volumes  and  upwards, 
Massachusetts  has  20,  containing  an  aggregate  of  614415 
vols. ;  Connecticut  6,  containing  102373 ;  Rhode  Island  3, 
containing  69868  ;  Maine  3,  containing  40700 ;  New  Hamp- 
shire 2,  containing  25679,  and  Vermont  1,  containing  10000. 
What  is  the  aggregate  number  of  volumes  in  these  libraries, 
and  how  many  more  in  the  libraries  of  Massachusetts  than  in 
those  of  all  of  the  other  New  England  States  ? 

23.  In  Illinois  in  1862  there  were  9811  public  schools, 
which  were  attended  by  519983  scholars.  What  was  the 
average  number  in  each  school  ] 

24.  A  man  invests  in  trade  at  one  time,  $680 ;  at  another 
time,  $820;  at  a  third  time,  $1580,  and  on  a  fourth  occasion 
$420.  How  much  must  he  add  to  the  sum  of  these  that  the 
amount  may  be  increased  three-fold  ? 

25.  The  Coast  Survey  issued  a  certain  number  of  hydro- 
graphic  maps  and  charts  in  1863,  of  which  3000  were  delivered 
to  the  marine  transportation  service,  4  times  as  many  +  300 
to  the  military  authorities,  and  the  remainder,  which  was  650 
less  than  one-half  the  whole  number  issued,  to  the  naval 
service.     What  number  of  maps  and  charts  were  issued  1 

26.  What  number  is  that  which,  being  divided  by  24,  the 
quotient  increased  by  25 -fl,  the  sum  diminished  by  the  dif- 
ference between  40  and  27,  the  remainder  multiplied  by  4, 
and  the  product  divided  by  11,  will  give  12  for  a  quotient? 

27.-  France,  with  a  population  of  36000000  in  1861,  had  a 
national  debt  of  $61.28  per  capita.  Required  her  national  debt. 


ARITHMETICAL   EXAMPLES.  23 

28.  The  annual  interest  upon  the  national  debt  of  France 
was  $110000000.  How  much  was  the  annual  interest  to  each 
person  ? 

*  29.  Colorado  Territory,  organized  Feb.  28,  1861,  was 
formed  of  47657000  acres  formerly  included  in  the  territories 
of  Utah  and  Kansas,  10262400  acres  in  that  of  Nebraska,  and 
8960600  acres  formerly  in  New  Mexican  territory.  Required, 
the  number  of  acres  and  square  miles  in  Colorado  Territory. 

30.  There  were  10869  miles  of  railway  in  Great  Britain  in 
1862,  the  receipts  from  which  were  28565355  pounds  sterling. 
Reckoning  a  pound  sterling  worth  $4.86,  how  many  dollars 
were  received  per  mile  1 

31.  A  man  worth  812750  received  a  legacy  of  88000  ;  he 
spent  8456  in  traveling,  and  gave  81000  to  a  college.  How 
much  money  had  he  left  1 

32.  The  number  of  1  and  2  cent  internal  revenue  stamps 
sold  in  1863  was  70036697,  the  value  of  which  was  81146- 
738.69 ;  the  number  of  3  to  20  cent  stamps  was  23065021, 
valued  at  81520440.18,  and  of  25  to  40  cent  stamps  3745355, 
worth  81009039.65.  Required,  the  number  and  value  of  the 
stamps  of  these  denominations. 

33.  Connecticut  made,  during  the  year  1863,  an  aggregate 
monthly  payment  of  870636  to  the  flimilies  of  8333  soldiers. 
How  much  was  the  average  amount  paid  to  the  family  of  each 
soldier  1 

34.  The  population  of  the  States  in  1860  was  31224885, 
there  being  241  representatives,  how  large  a  represen- 
tation should  New  York  have,  whose  population  was 
3880735  ? 


35.  Divide  900 +  (34  + 2)  X  5  by  (75-r5) +(4x  12)-33. 

36.  In  Vermont  during  the  month  of  August,  1863,  7071 
men  were  drafted ;  3583  of  these  were  exempted,  557  failed 
to  report,  145  cases  were  undecided,  and  5  died ;  the  remain- 
der were  held  to  military  service ;  of  these  1833  paid  com- 


24  ARITHMETICAL    EXAMPLES. 

mutation,  and  630  furnished  substitutes.     How  many  entered 
the  service  personally  1 

37.  There  is  an  island  40  miles  in  circumference.  A  and 
B  commence  traveling  around  it  at  the  same  time  and  place, 
but  in  different  directions,  A  at  the  rate  of  4  miles  an  hour, 
and  B,  5  miles.  How  far  apart  will  they  be  at  the  end  of  7 
hours  *? 

38.  The  entire  coinage  of  the  U.  S.  Mint  and  branches  from 
the  commencement  of  their  operations  till  June  30,  1863,  was 
as  follows :  At  Philadelphia,  768279944  pieces  were  coined, 
valued  at  1509602439.14 ;  at  San  Francisco,  15136912  pieces, 
worth  $165459288.20;  at  New  Orleans,  94890695  pieces, 
worth  170271652.13;  at  Charlotte,  1206954  pieces,  worth 
$5048641.50;  at  Dahlonega,  1381750  pieces,  worth  $6121- 
919.00  ;  and  at  the  Assay  Office,  New  York,  gold  and  silver 
in  various  forms  worth  $133131557.35.  Required  the  whole 
number  of  pieces  and  their  value. 

39.  A  grocer  bought  25  barrels  of  sugar  at  $25  a  barrel, 
and  34  barrels  at  $22  a  barrel.  How  much  would  he  gain 
by  selling  the  whole  at  $27  a  barrel  1 

40.  What  is  the  area  of  New  England,  the^e  being  in 
Maine,  31766  square  miles ;  in  Vermont,  9056 ;  in  New  Hamp- 
shire, 9280;  in  Massachusetts,  7800;  in  Rhode  Island,  1046; 
and  in  Connecticut,  4730 1 

41.  The  cavalry  and  artillery  furnished  by  Illinois  up  to 
Jan.  1,  1863,  amounted  to  20916  men,  and  the  cavalry  was 
12918  more  than  the  artillery;  the  infantry  was  985  more 
than  7  times  the  cavalry.  How  many  men  had  Illinois  fur- 
nished for  the  war,  Jan.  1,  1863  1 

42.  A  drover  bought  cattle  for  $19800,  and  sold  a  certain 
number  of  them  for  $15360,  at  $96  per  head,  gaining  thereby 
$960.  How  much  did  he  gain  per  head,  and  how  many  cattle 
did  he  buy  1 

43  The  exports  of  flour  and  wheat  from  the  United  States 
to  Great  Britain  were  as  follows:  in  1861,2561661  barrels 


ARITHMETICAL    EXAMPLES.  25 

of  flour,  and  255539T0  bushels  of  Vvheat;  in  1862,  26T2515 
barrels,  and  25754709  bushels ;  in  1863, 1479413  barrels,  and 
23107190  bushels.  How  many  more  bushels  of  wheat  than 
barrels  of  flour  were  exported  in  the  three  years  ? 

44.  Bought  600  bushels  of  potatoes  for  $540,  and  sold  360 
buohels  at  11.25  per  bushel,  and  the  remainder  at  cost.  How 
much  was  gained  by  the  transaction  ? 

45.  In  1862  Ohio  sowed  09374  acres  of  barley,  from  which 
763114  bushels  were  produced;  2266129  acres  of  corn  were 
planted,  which  yielded  74782257  bushels.  How  much  greater 
was  the  yield  of  corn  than  barley  per  acre  ? 

46.  Jan.  1,  1863,  there  were  507  banlcs  in  the  Eiistern 
States,  491  in  the  Middle  States,  167  in  the  Southern  States, 
807  in  the  Western  States.  How  many  more  banks  in  the 
Eastern  and  Middle  States  than  in  the  Southern  and  Western 
States  ? 

47.  The  sum  of  the  killed  and  prisoners  in  the  Union  army 
at  the  battle  of  Stone  River  was  3496,  and  the  prisoners  were 
548  more  than  the  killed.  The  wounded  were  747  more 
than  three  times  the  prisoners.  The  Vrdiole  Union  force  en- 
gaged being  43500,  how  many  were  left  for  duty  after  the 
battle  ? 

48.  In  1864  there  were  237  members  of  Congress,  and  the 
salary  of  each  member  was  $3000.  How  much  did  they  all 
receive  ? 

49.  The  United  States  contain  an  area  of  2819811  square 
miles,  and  in  1860  there  were  1 1  inhabitants  to  the  square 
mile.     What  was  the  entire  population  ? 

50.  The  New  England  States  have  35  libraries,  containing 
863035  vols. ;  the  Middle  States,  28,  containing  763733  ;  the 
Southern  States,  24,  containing  503563,  and  the  Western 
States,  17,  containing  273109.  What  is  the  average  number 
of  volumes  in  these  libraries  ? 

^   51.  A  mechanic  earns  |75  a  month,  but  his  necessary  ex- 

2 


26  ARITHMETICAL    EXAMPLES. 

penses  are  $50  per  month.     IIovv-  long  will  it  take  him  to  pay 
for  a  flirm  of  GO  acres  worth  $40  an  acre  ? 

52.  A  grocer  wishes  to  put  1280  pounds  of  tea  in  4  kinds 
of  boxes,  containing  respectively  7,  9,  10  and  14  pounds,  using 
the  same  number  of  boxes  of  each  kind.  How  many  boxes 
can  he  fill  ? 

53.  In  1860  there  were  made  in  the  United  States  1830000 
gallons  of  wine,  valued  at  $2,50  per  gallon.  Plow  many 
school  houses,  worth  $?50  each,  could  be  built  with  the  pro- 
ceeds ? 

54.  The  United  States  paid  $61000  for  the  site  of  the  Cus- 
tom House  at  Richmond,  Va.,  and  contracted  for  the  building 
for  $110000;  the  total  expense  to  the  Government  June  1, 
1861,  was  $252016.  How  much  did  the  cost  exceed  the 
price  agreed  upon  ? 

55.  The  population  of  New  Orleans  in  1850  was  116375  ; 
in  1855,  139190,  and  in  i860,  168675.  How  much  move 
was  the  increase  in  the  last  five  years  than  in  the  previous 
five  years  ? 

56.  In  1861  the  importation  of  specie  into  the  United  States 
was  $46339611,  and  the  exportation  $29791080.*  What  was 
the  excess  of  importation  over  exportation  1 

57.  $16415052  specie  was  imported  in  1862,  and  $36886950 
was  exported.  How  much  more  was  the  excess  of  exporta- 
tion in  1862  than  the  e:?icess  of  importation  in  1861  1 

58.  In  1863,  $9555648  specie  was  imported,  and  $64156610 
was  exported.  What  was  the  excess  of  exportatioti  over  im- 
portation for  the  three  years  ? 

59.  In  1862  there  were  sent  out  from  the  Dead  Letter  Office 
for  delivery  10475  letters,  containing  $46538.90  ;  of  these 
8766,  containing  $41068.48  were  delivered,  1593,  containing 
$5095.74  were  returned  to  the  office,  and  guerillas  appropri- 
ated the  remainder.  What  was  the  average  amount  in  each 
letter  lost  1 


ARITHMETICAL    EXAMPLES.  27 

60.  Gunpowder  was  invented  in  the  year  1330.  Iron  was 
•^discovered  B.  C.  1406.  What  period  of  time  elapsed  between 
these  two  events  1 

Gl.  Of  the  appropriation  for  the  Custom  House  in  Galveston, 
$1640.18  was  unexpended,  86000  was  paid  for  the  site,  and 
the  building  cost  •$17850,75  more  than  tlio  contracted  price, 
which  was  $90509.07.     AVliat  was  the  appropriation  ? 

62.  M.  Smith  rented  a  sus^ar  orchard  containino;  1500 
trees,  agreeing  to  assume  all  the  necessary  expenses  in  making 
sugar,  for  one-half  the  quantity  made  ;  he  made  on  an  average 
3^  lbs.  to  each  tree,  and  sold  his  part  of  the  first  3000  lbs. 
made  for  25  cents  a  pound,  and  the  remainder  at  20  cents; 
he  paid  $60  for  labor,  $30  for  team  work,  and  burned  25 
cords  of  wood  worth  $2  a  cord.     How  much  was  his  gain  1 

63.  A  horse  dealer  gave  $8448  for  a  certain  number  of 
horses ;  he  sold  a  part  of  them  for  $7650  at  $90  each,  and  by 
so  doing  lost  $6  a  head.  For  how  much  must  he  sell  the  re- 
mainder per  head  to  gain  $252  on  the  whole  ? 

64.  The  expenditures  of  the  Post  Office  Department  in 
1860  were  $14874772.89,  and  the  gross  revenue  $9218087.40. 
How  much  greater  than  the  revenue  were  the  expenditures  ] 

65.  In  1861  the  expenses  of  the  Post  Office  Department 
were  $13606739.11,  and  the  gross  revenue,  $9049296.40. 
How  much  more  had  the  expenditures  decreased  than  the 
revenue  from  the  previous  year  1 

6Q.  In  1062  the  expenditures  were  $11125364.13,  and  the 
revenue  $9012549.56.  How  much  nearer  self-supporting  was 
the  Post  Office  Department  in  1862  than  in  1861  ? 

67.  In  Massachusetts  32079  men  were  drafted  in  1863;  of 
these  22343  were  exempted,  3046  failed  to  report,  and  the 
remainder  were  held  for  service ;  of  these  743  served  person- 
ally, 2325  furnished  substitutes,  and  the  remainder  paid  $300. 
How  much  commutation  money  did  the  Government  receive? 

68.  Jan.  1,  1863,  Rhode  Island  had  furnished  3147  men  for 


28  ARITHMETICAL    EXAMPLES. 

three  months,  2069  for  nine  months,  and  9410  for  three  years ; 
durmg  the  year  1863,  1246  men  were  obtained  by  draft,  716 
recruits  were  sent  to  regiments  in  the  field,  and  two  new  regi- 
ments were  formed,  containing  1800  men;  425  enlisted  in 
other  States,  and  1400  were  in  the  navy.  What  was  the 
aggregate  number  of  men  furnished  by  Rhode  Island  for  the 
war  up  to  Jan.  1,  1864? 

v^  69.  What  must  the  number  be  which  divided  by  453,  will 
give  the  quotient  807,  and  the  remainder  109  ? 

70.  A  has  1310;  B,  $558,  and  C,  $744,  with  which  they 
agree  to  purchase  horses  at  the  highest  price  per  head  that 
will  allow  each  man  to  invest  all  his  money.  How  many 
horses  can  each  man  buy  % 

71.  Of  S003  cases  admitted  into  the  retreat  fjr  the  insane 
at  Hartford,  Connecticut,  574  were  married  males,  and  728 
were  single,  704  were  married  females,  and  730  single ;  the 
remainder  were  widovred;  the  whole  number  of  females  ex- 
ceeded the  whole  number  of  males  by  279.  Required  the 
number  of  widowecl  males  and  females, 

72.  The  receipts  of  the  U.  S.  Treasury  for  1863  were  as 
follows:  Customs,  169059642;  Public  LandS,  $167617; 
Direct  Tax,  $1485104  ;  Internal  Revenue,  $37640788  ;  Mis- 
cellaneous, $3046615;  Loans,  $776682362.  Required  the 
total  receipts. 

73.  The  expenditures  for  the  same  period  were  as  follows  : 
Civil  List,  $6350618.78;  Foreign  Intercourse,  $1231413.06; 
Miscellaneous,  $15671890.24;  Interior  Department,  $4210- 
520.79^;  War  Department,  $599298600.83 ;  Navy,  $63211- 
105.28*;  on  account  of  Public  Debt,  $205816482.  Required 
the  aggregate  expenditures. 

74.  The  balance  in  the  Treasury  at  the  beginning  of  the 
year  was  $13043547.  AVhat  was  the  balance  at  the  end  of 
the  year,  the  receipts  and  expenses  being  as  is  stated  in  the 
preceding  examples  % 

75.  The  State  of  Delaware  received  $60385.51  for  general 


ARITHMETICAL    EXAMPLES.  29 

expenditures,  in  1861,  and  837424.99  for  educational  purposes; 
the  expenditures  for  general  purposes  were  $38989.05,  and 
so  much  was  expended  for  school  purposes  that  the  balance 
in  Treasury  Jan.  1,  1862,  was  821390.46.  Required  the 
sum  expended  for  education  ? 

73.  The  gold  coin  made  at  the  U.  S.  Mint  in  Philadel- 
phia in  1863  was  as  follows:  152963  double  eagles,  3658 
eagles,  6902  half  eagles,  39  three-dollar  pieces,  20990  quar- 
ter-eagles, and  1950  dollar  pieces.  "What  was  the  whole 
number  of  pieces  made  and  their  value  1 

77.  The  silver  coin  made  at  the  mint  in  Philadelphia  in 
1863  was  as  follows:  31400  dollars,  425260  half-dollars, 
412860  quarter-dollars,  49460  dimes,  64460  half-dimes,  and 
93460  three-cent  pieces.  Required  the  whole  number  of 
pieces  and  their  value. 

78.  At  the.  branch  mint  in  San  Francisco  in  1863,  866423 
double-eagles  were  coined,  9000  eagles,  16500  half  eagles, 
and  4000  quarter-eagles.  Required  the  number  of  pieces 
and  their  value. 

79.  During  the  year  1863  there  were  coined  at  the  branch 
mint  in  San  Francisco,  1542000  half-dollars,  4S00O  quarter- 
dollars,  291250  dimes,  and  100000  half-dimes.  How  many 
pieces  of  silver  v/ere  coined,  and  what  was  their  value? 

80.  In  1863,  47845000  cents  were  coined  in  the  United 
States;  $1949877.90  of  gold  and  $390204.42  of  silver  were 
coined  at  the  Assay  Office,  New  York ;  the  coinage  of  the  U. 
S.  Mint  and  branches  being  as  stated  in  the  four  preceding 
examples  ;  what  was  the  value  of  the  entire  coinage  of  1863  ? 

81.  A  flour  merchant  bought  2000  barrels  of  flour  at  89  a 
barrel,  and  sold  1200  barrels  at  810,  and  the  remainder  at  88 
a  barrel.     How  m.uch  was  his  gain? 

82.  What  was  the  value  of  gold  and  silver  of  domestic 
production  in  1863,  if  $2093500.69  was  deposited  at  the 
mint  in  Philadelphia,  818207316.21  at  San  Francisco,  and 
81379448.60  at  the  Assay  Oftice.  New  York  .? 


30  APJTHMETICAL    EXAMPLES. 

83.  The  sum  of  two  numbers  is  2487,  and  the  greater  is 
553  more  than  the  less.     What  are  the  numbers  1 

84.  The  Internal  Revenue  collected  for  the  year  ending 
June  30,  18G3,  was  $40993954.97.  The  total  receipts  to 
Aug.  31,  1863,  were  $47489473.03  ;  to  Sept.  30,  $53625078.- 
46.  How  much  less  was  received  in  September,  than  in  July 
and  August  ? 

85.  A  cistern  containing  1260  gallons  has  two  pipes.     By 
\/the  first  48  gallons  run  into  the  cistern  every  half  hour,  and 

by  the  second  36  gallons  run  out  in  an  hour.     In  how  many 
hours  will  the  cistern  be  filled  ? 

86.  A  man  sold  600  bushels  of  wheat  at  $1.50  a  bushel, 
and  took  his  pay  in  sugar  at  12  cents  a  pound  ;  he  afterward 
sold  one-half  his  sugar.     How  much  had  he  left  ? 

87.  The  number  of  m.en  sent  by  Vermont  to  the  war  was 
as  follows :  One  regiment  of  3-month3  men,  numbering  782  ; 
5  regiments  of  9-months  troops,  containing  4833  men ;  one 
regiment  of  cavalry,  966  strong;  2  batteries,  containing  286 
men;  3  companies  of  sharpshooters,  averaging  100  men 
each;  10  regiments  of  3-years  men;  and  2740  recruits  for 
regiments  in  the  field ;  making  the  total  numbertJf  men  fur- 
nished for  the  v/ar,  up  to  Oct.  1st,  1863,  19607.  What  was 
the  average  strength  of  the  3-years  regiments  1 

88.  The  quota  of  Vermont  under  the  fn\st  call  for  500000 
8-years  volunteers  was  8950  ;  under  the  second  call  for  300000 
3-years  volunteers,  4898,  and  the  same  under  the  call  for 
300000  9-month3  volvmteers.  To  meet  the  first  two  requisi- 
tions the  State  furnished  13992  men,  and  under  the  last  call 
4834  9-months  men.  How  much  in  excess  of  her  quota  Avtis 
Vermont,  4  9-months  men  being  equivalent  to  1  3-years  man  1 

89.  From  340  -|-  (20-4)  x  (8  +  2)  take  36-^3  -f  (28  x  6)  -^ 
(19-5.) 

90.  A  tailor  made  2804  pairs  of  pants  in  four  successive 
years,  making  each  year  50  pairs  more  than  during  the  pre- 
vious year.     How  many  pairs  did  he  make  each  year  ? 


ARITHMETICAL    EXAMPLES.  31 

91.  The  expenditures  for  educational  purposes  in  New  York 
for  the  year  1861,  were  83842270.81  ;  in  New  Jersey,  .15540- 
283.80 ;  in  Pennsylvania,  $2389383.60,  and  in  Delaware, 
885333.03.  How  much  more  v.as  expended  in  New  York 
than  in  the  other  three  States  ? 

92.  The  State  debt  of  Maine  at  the  outbreak  of  the  rebel- 
lion stood  as  follows :  Debt  incurred  during  the  Aroostook 
war,  $449000 ;  debt  due  Massachusetts  for  lands,  $^250000. 
The  war  debt  for  1861  was  ^800000  ;  during  1862,  $27000  of 
this  debt  was  paid,  and  there  was  added  to  the  war  debt  in 
1863,  $950000.  What  was  the  total  debt  of  the  State,  Jan.  1, 
1863,  and  Jan.  1,  1864? 

93.  How  many  pounds  of  sugar  at  20  cents  per  pound, 
must  be  given  for  5  pieces  of  cotton  cloth,  containing  44 
yards  each,  at  42  cents  a  yard  ? 

94.  A  man  bought  750  acres  of  land  at  $20  per  acre ;  he 
sold  at  one  titne  325  acres  at  $23  per  acre,  at  another  time 
260  acres  at  $25  per  acre.  At  what  price  per  acre  must  he 
sell  the  remainder  to  gain  on  his  purchase  $1945  ? 

95.  According  to  the  census  of  1860,  there  were  in  the 
United  States  13869434  white  males  and  13133890  females; 
234000  free  colored  males  and  253996  free  colored  females; 
1982625  male  slaves,  and  1971135  female  slaves.  How 
many  more  males  than  females  in  the  United  States  ] 

96.  250  X  6-^(4  x  16)"^ (8  x  2)  +  (25  x  (8  -^  4))=:  how 
many  ? 

97.  In  1860  New  Jersey  cultivated  1039086  acres,  worth 
$180281421  ;  Maryland  cultivated  the  same  year  1833306 
acres,  worth  $145976990.25.  Hov,r  much  were  the  farms  of 
New  Jersey  worth  per  acre  more  than  those  of  Maryland  1 

98.  Divide  16  x  72  x  45  x  21  by  27  x  32  x  12  x  35. 

99.  The  rebel  army  in  the  battle  of  Stone  River  lost  one- 
fourth  of  all  its  forces  engaged ;  3500  were  taken  prisoners, 
and  four  times  this  number  w^as  2000  more  than  the  killed  and 
wounded.     Required  the  Confederate  force  in  the  battle. 


32  ARITHMETICAL    EXAMPLES. 

100.  Bought  CO  yards  of  cloth  at  the  rate  of  2  yards  for 
$5,  and  80  yards  more  at  the  rate  of  4  yards  for  eif,9 ;  I  im- 
mediately sold  the  whole  at  the  rate  of  5  yards  for  814;  how 
much  did  I  gain  1 

101.  The  fjuota  of  New  Jersey  under  the  various  calls  for 
troops  was  as  follows:  1st  requisition,  3123  ;  2d,  3138;  3d, 
5230;  4th,  .5230;  and  5th,  (drafted  militia,)  10478.  -Under 
the  first  call  she  furnished  3105  men;  2d,  3120;  3d,  7601 ; 
4th,  4644;  5th,  10714,  and  1030  recruits  for  old  regiments 
in  the  field  were  enlisted.  How  much  in  excess  of  her  quota 
was  New  Jersey,  Jan.  1,  1863  ? 

102.  Connecticut  cultivated  in  1802,  1830800  acres,  laid 
out  in  22885  farms,  the  total  value  of  which  was  $91540000. 
What  v/as  the  average  value  of  each  flirml  Average  num- 
ber of  acres  in  each  farm  1  v 

103.  A  farmer  exchanged  40  bushels  of  corn  and  oats, 
mixed  in  equal  quantities,  at  11.25  and  $.95  per  bushel 
respectively,  for  whe^^t  and  rye  in  equal  quantities,  at  $2.25 
and  12.15  per  bushel  respectively.  How  many  bushels  of 
wheat  and  rye  did  he  obtain  '? 

104.  Arkansas  Post  surrendered  to  Gen.  McClera«ind,  Jan. 
11,  1863.  The  rebel  loss  in  killed  and  wounded  was  550, 
which  was  twice  the  Union  loss,  and  the  number  of  prisoners 
was  230  less  than  6  times  the  loss  in  killed  and  wounded  of 
both  armies.     Vv^hat  was  the  number  of  prisoners  ? 

105.  A  firmer  bought  an  equal  number  of  horses,  sheep 
and  hogs  for  $9600.  He  gave  $108,  $9  and  $11  per  head  for 
them  respectively.     Yf  hat  was  the  number  of  animals  bought  ? 

106.  The  population  of  the  five  largest  cities  in  England  in 
1861  was  as  follows  :  London,  2803034 ;  Liverpool,  443874  ; 
Manchester,  338346 ;  Birmingham,  29.5955;  Leeds,  207153. 
How  many  more  inhabitants  in  London  than  in  the  four  other 
cities  1 

107.  A  and  B  invested  $120  in  lottery  tickets,  A  paying  $3 
as  often  as  B  $5.     C  and  D  invested  an  equal  sum,  C  paying 


ARITHMETICAL    EXAMPLES.  33 

S4  as  often  as  D  paid  $6.  They  purchased  tickets  together 
agreeing  to  share  the-prizes  in  proportion  to  the  siinis  invested 
by  each.  The  prizes  amonilted  to  87200.  How  much  ought 
each  to  receive  ? 

108.  The  aggregate  receipts  of  the  Post  Office  Depart- 
ment for  13Go  were  $11163789.59,  while  the  expenditures 
during  the  same  time  were  $11314206.84.  What  was  the 
net  expense'^ 

109.  A  company  in  a  fort  numbering  75  men  have  provi- 
sions for  30  days.  How  many  men  must  depart,  that  the 
same  may  last  the  remainder  45  days  1 

110.  The  rebel  loss  at  Gettysburg  was  reported  40121; 
the  prisoners  were  371  more  than  half  the  loss  in  killed 
and  wounded,  and  4  times  the  killed  was  1000  more  than  the 
wounded.  What  were  the  respective  losses  in  killed,  wounded 
and  prisoners  ? 

111.  A  m.erchant  expended  for  cloth  $7850.  He  sold  a 
certain  number  of  yards  for  $5580,  at  $15  per  yard,  and 
gained  on  those  sold  $1860.  How  many  yards  did  he  buy  at 
first,  and  how  much  did  he  gain  per  yard  on  the  cloth  sold  ? 

>/"  112.  A  horse  worth  $120,  and  4  cows  at  $28  each,  were 
exchanged  for  31  sheep  and  $4G  in  money.  What  were  the 
sheep  valued  at  per  head  '? 

113.  The  quotient  of  one  number  divided  by  another  is 
74,  the  divisor  is  321,  and  the  remainder  95.  What  is  the 
dividend  1 

114.  Tlie  mails  of  the  United  States  in  1332  vrerc  carried 
2001500  miles  by  steamboat,  at  an  expense  of  $300225  ;  by 
coaches  7263400  miles,  for  $1744416,  and  by  railroad  22777- 
200,  for  which  $2505492  were  paid.  How  much  was  the 
rate  per  mile  by  each  mode  of  transportation  1 

115.  General  Meade  reported  the  losses  of  the  Union  army 
at  Gettysburg  23186.  The  number  killed  was  290  more 
than   one-eighth  of   the  sum   of  the  losses  in  prisoners  and 

2* 


34  ARITHMETICAL    EXAMPLES. 

wounded,  and  twice  the  prisoners  was  423  less  than  the 
wounded.  How  many  were  the  killed,  wounded  and  pris- 
oners ? 

116.  Bought  17  cwt.  of  prunes  at  ^15  per  cwt.,  and  gave 
in  exchange  for  them  250  lbs.  of  butter  at  25  cents  per 
pound,  48  dozen  eggs  at  15  cents  per  dozen,  and  the  remain- 
der in  salt  at  $1.70  per  bushel.  How  many  bushels  of  salt 
were  required  ? 

117.  The  population  of  the  seven  largest  cities  in  France 
in  1861  was  as  follows:  Paris,  1696141  ;  Lyons,  318803; 
Marseilles,  260910;  Bordeaux,  162750;  Lille,  131827; 
Nantes,  112625;  Toulouse,  113229.  How  much  did  the 
population  of  Paris  exceed  that  of  the  other  six  cities  ? 

118.  What  is  the  value  of  16  x  3125— (49  x  7)  + (125  x 
27)— (9  X  32)  +43264— 16  x  9  ? 

119.  A  trader  purchased  a  lot  of  horses  and  oxen  for 
12000,  paying  twice  as  much  for  a  horse  as  for  an  ox.  There 
were  three  times  as  many  oxen  as  horses,  and  the  horses  cost 
him  1^80  a  head.     Required  the  number  of  each. 

120.  Required  the  area  of  North  America,  if  tl^  United 
States  contain  2988892  square  miles ;  British  America, 
2914318;  Danish  America,  800000;  Russian  America,  394- 
000;  Mexico,  645822 ;  and  Central  America,  219000. 

121.  S.  J.  Eaton  bought  75  hhds.  molasses  at  118  per 
hhd.  How  much  must  lie  charge  per  hhd.  to  gain  ^300,  and 
what  will  be  the  gain  on  each  ? 

122.  What  were  the  respective  losses  in  the  Union  army 
in  the  battle  of  Chickamauga,  3  times  the  killed  being  13  less 
than  the  missing,  and  twice  the  missing  being  628  more  than 
the  wounded,  and  the  whole  loss  15851  ? 

123.  If  the  President  of  the  United  States  expends  daily 
160,  how  much  will  he  be  able  to  save  at  the  end  of  four 
years,  his  salary  being  $25000  per  annum  ? 

124.  The  army  pension  rolls   stood  as  follows,  June  30, 


ARITHMETICAL    EXAMPLES.  35 

ISGo  :  Invalid  pensioners  7248,  to  whom  -^570048  was  pay- 
able annually  ;  Revolutionary  soldiers,  18,  to  v.hom  ^^1045 
was  payable  ;  vv'idows  of  Revolutionary  soldiers-,  1573,  amomit 
payable  to  them  8129G84;  widows,  mothers,  sisters  and 
orphans,  in  wars  since  the  Revolution,  4820,  annual  payment 
to  the  same  ^526266.  Yv'hat  v/as  the  whole  number  of  pen- 
sioners and  the  sum  paid  them  ? 

125.  I  exchanged  5  barrels  of  vinegar,  each  containing  32 
gallons,  at  25  cents  a  gallon,  for  5  pieces  of  sheeting,  each 
contahiing  40  yards.     How  much  did  it  cost  me  per  yard  ? 

126.  In  1860  Virginia  contained  19578064  acres  of  im- 
proved land,  worth  ^371608736.72;  Pennsylvania,  6548847 
acres,  worth  ^662022943.23.  How  much  more  were  the 
flirms  worth  per  acre  in  the  latter  State  than  in  the  former  ? 

127.  Required  the  actual  value  of  my  farm  if  $25344  is  6 
times  the  sum  I  paid  for  it,  and  it  cost  me  '^776  less  than  its 
real  value. 

128.  According  to  the  census  of  1S60,  20875  of  the  popu- 
lation of  New  York  city  were  born  in  the  Eastern  States, 
897980  in  the  Middle  States,  1941  in  the  Western  States, 
4881  in  the  Border  States,  1353  in  the  Seaboard  Slave  States, 
882  in  the  Southwest  Slave  States,  and  2130  in  the  territo- 
ries. How  many  of  the  inhabitants  of  the  city  were  natives 
of  the  United  States  ? 

129.  The  foreign  born  in  New  York  city  in  1860  were  as 
follows:  natives  of  German}^,  119984;  of  Great  Britain,  244- 
826;  of  Contmental  Europe^  17235,  and  of  various  other 
countries  1072.     Required  the  total  foreign  born. 

130.  The  population  of  the  city  was  629904  in  1855.  How 
much  was  the  increase  in  5  years,  the  population  in  1860 
being  as  stated  in  Examples  123  and  129'? 

131.  Ten  men  ngrecd  to  gather  1000  bushels  of  cranberries, 
and  to  receive  for  their  labor  one-half  the  quantity  gathered. 
After  400  bushels  were  gathered  4  men  withdrew,  Icciving  the 


3G  ARITHMETICAL    EXAMPLES, 

Others  to  complete  the  job.     How  many  bushels  should  each 
man  receive  1  * 

132.  P.  Harriman  purchased  318  acres  of  wild  land  for 
$6996,  and  sold  253  acres  at  ^I?17  per  acre,  and  the  remainder 
at  cost.     Did  he  gain  or  lose,  and  how  much  1 

133.  Durmg  tlie  year  1803  $2876983  was  paid  to  post- 
masters, and  $6541580  for  mail  transportation.  Xhe  expen- 
ditures bemg  $150417  in  excess  of  the  revenue,  which  was 
$11163789.  How  much  was  expended  for  miscellaneous 
purposes  1 

134.  Having  money  to  invest  I  buy  2  farms  worth  $4550 
f"    each,  20   shares  railroad  stock  at  $106  per  share,  and  have 

$250  left.     How  much  had  I  at  iirst  1 

135.  The  navy  pension  rolls  for  1863  showed  that  545  navy 
invalids  were  paid  $35019;  577  widows  or  children  were 
paid  $107886,  and  10  privateer  pensioners  were  paid  $622. 
How  many  pensioners  were  there,  and  what  was  the  amount 
paid'? 

136.  How  many  barrels  of  apples  at  $4  per  barrel  must 
be  given  in  exchange  for  10  bags  of  wheat,  each  cont^^ining  3 
bushels  at  $2  per  bushel  ? 

137.  During  the  first  three  months  of  1864  there  were  27 
gold  mining  companies  organized  in  New  York  city,  with  an 
average  capital  of  $2350000;  4  silver  companies,  with  an 
average  capital  of  $3625000 ;  8  coal  and  iron  companies, 
whose  average  capital  was  $1250000.  and  4  copper  companies, 
with  an  average  capital  of  $625000.  How  much  capital  was 
invested  in  mining  companies  during  the  three  months  ? 

138.  What  is  the  number  of  subjects  belonging  to  the 
Eussian  Government,  there  being  66891493  in  Europe,  8203- 
197  in  Asia,  and  54000  in  America? 

130.  How  many  sheep  at  $3.62^  must  be  given  in  exchange 
for  58  cows  at  $40  each  ? 
V      140.  The  first  settlement  in  the  United  States  was  made 


ARITHMETICAL    EXAMPLES.  37 

in  1565.  America,  was  discovered  by  Columbus  in  1492. 
How  many  more  years  from  the  first  settlement  to  the  Dec- 
laration of  Independence  in  1770,  than  from  the  discovery  to 
the  first  settlement  1 

141.  A  grocer  in  packing  6  dozen  dozen  eggs,  broke  half  a 
'^ozen  dozen,  and   sold  the  remainder  at  20  cents  a  dozen. 

How  much  did  .he  receive  for  the  eggs  1 

142.  What  are  30  hogsheads  of  molasses  worth  at  8.75  a 
gallon,  if  each  hogshead  contains  G8  gallons  1 

143.  A  speculator  paid  865G9.04  for  a  quantity  of  wheat ; 
he  sold  1480  bushels  at  82  a  bushel,  and  the  remainder  stood 
him  in  81.42  a  bushel.     How  many  bushels  did  he  purchase? 

144.  During  the  year  1SG2,  G0021250  l-cent,  183740250 
3-ce.nt,  1029300  5-cent,  4058450  10-cent,  1046750  12-cent, 
984125  24-cent,  396040  30-cent,  and  30940  90-cent  stamps 
were  issued  by  the  Post  Office  Department.  Required  the 
whole  number  of  stamps  and  their  value. 

145.  During  the  same  year  the  following  number  of 
stamped  envelopes  were  issued:  l-cent,  3084400;  3-cent, 
20963050;  4-cent,  35000 ;  6-cent,  131850 ;  10-cent,  520050 ;  12- 
cent,  8400 ;  20-cent,  7850 ;  24-cent,  8800 ;  40.cent,  4100,  and 
195800  letter  sheets  and  -stamped  envelopes  combined  ;  the 
total  value  of  all  was  8733265.50.  What  was  the  value  of 
the  combined  letter  sheets  and  envelopes  1 

146.  During  the  same  time  2364850  l-cent  newspaper 
wrappers  were  issued.  Vf  hat  were  the  total  receipts  from 
stamps,  stafnped  envelopes  and  wrappers  1 

147.  The  receipts  from  stamps  in  1861  were  85908522.60, 
and  from  envelopes,  8781711.13.  The  receipts  in  1862  from 
the  same  sources  being  as  stated  in  previous  examples,  how 
much  more  was  received  in  1862  than  in  18G1  ? 

148.  A  grocer  gave  153  barrels  of  flour  vrorth  89  a  barrel 
for  81  barrels  of  sugar  containing  l'"0  pounds  each.  What 
was  the  cost  of  the  sugar  per  pound  1 

149.  In   1861,  10631  vessels,  tonnage   1024726,  arrived  in 


66  ARITHMETICAL    EXAMPLES. 

the  ports  of  Russia ;  10739  vessels,  tonnage  1026794,  departed 
from  the  same  ports.     What  was  the  average  tonnage  of  the 

vessels  ? 

150.  If  850  men  require  25500  lations  of  bread  for  a 
month,  how  many  rations  will  a  garrison  of  1250  men  re- 
quire for  the  same  time  1 

151.  In  the  month  of  Sept.  1863,  on  account  of  the  Indian 
massacre,  6588  fugitives  fled  from  the  St.  Peters  district  in 
Minnesota,  one-ninth  as  many  from  the  Minneapolis  district, 
and  in  other  districts  127  more  than  from  Minneapolis.  How 
many  were  made  homeless  by  this  massacre  ? 

152.  From  Jan.  1,  to  April  15,  1864,  27  gold  mining 
companies  were  organized  in  New  York  with  an  aggregate 
capital  of  $63450000.  What  was  the  average  capital  of  each 
company  ? 

153.  Two  persons,  starting  from  the  same  place  and  travel- 
ing in  opposite  directions,  are  20  miles  apart  at  the  end  of 
one  hour,  but  traveling  in  the  same  direction  they  are  6  miles 
apart  at  the  end  of  an  hour.  How  far  does  each  travel  per 
hour  1  ' 

154.  The  population  of  France  in  1861  was  37472732;  of 
Algeria,  2999124;  and  of  French  colonies,  3062389.  How 
many  subjects  had  the  French  government  1     . 

155.  Three  men  rented  a  farm  and  raised  960  bushels  of 
grain,  which  was  divided  in  proportion  to  the  rent  paid  by 
each ;  the  first  was  to  have  one-half  of  the  whole;  the  second 
two-thirds  of  the  remainder,  and  the  third  what  was  left. 
How  much  did  each  receive,  the  grain  being  worth  ^2  a 
bushel  ? 

156.  During- the  year  ending  July  1,  1862,  9763  letters 
containmg  papers  of  value  other  than  money,  were  sent  to  the 
dead  letter  oflice,  and  the  following  reasons  were  assigned  for 
their  non-delivery:  Held  for  postage,  1050 ;  misdirected, 
1466 ;  mails   suspended,    326 ;    refused,    26 ;    name   of  post 


ARITHMETICAL    EXAMPLES.  39 

office  omitted,  86 ;  person  addressed  dead,  27 ;  and  the  others 
were  uncalled  for.  How  many  of  this  last  number  were 
there  ? 

157.  Gen.  Grant  reported  the  losses  of  the  Union  army  in 
the  series  of  battles  connected  with  the  taking  of  Vick'sburg 
as  follows:  Port  Gibson,  130  killed,  71S  wounded,  and  5 
missing;  Raymond,  73  killed,  365  wounded,  and  32  missing; 
Jackson,  40  killed,  240  wounded,  6  missing ;  Champion's 
Hill,  426  killed,  1842  wounded,  189  missing;  Big  Black 
Bridge,  29  killed,  242  wounded,  2  missing,  and  the  losses 
before  Vicksburg  made  tha.  entire  loss  8875.  This  was  so 
distributed  that  the  total  missing  were  706  less  than  the 
killed,  and  the  wounded  were  25  less  than  4  times  the  sum 
of  the  killed  and  missing.  Required  the  number  of  killed, 
wounded  and  missing  before  Vicksburg. 

158.  The  forward  wheels  of  a  carriage  are  7  feet  in  circum- 
ference, and  the  hind  wheels  10.  How  many  times  will  each 
revolve  in  passing  over  42  miles,  there  being  5280  feet  in  a 
mile  ? 

159.  A'man  paid  ^1024  for  a  farm,  8250  for  drainage,  850 
for  fencing,  and  for  hired  labor,  8376.  The  gross  proceeds  of 
one  year  amounted  to  82100  ;  with  the  profits  he  purchased 
an  equal  number  of  sheep  at  83  each,  and  horses  at  877  a 
piece.     How  many  of  each  did  he  buy  1 

160.  The  population  of  Great  Britain  and  Ireland  in  1863 
was  estimated  at  30000000,  and  the  value  of  real  and  per- 
sonal property,  833402600000  ;  at  the  same  time  the  estimated 
population  of  the  loyal  States  was  24000000,  and  the  value 
of  property,  813929840000.  How  much  more  property  to 
each  person  in  the  United   Kingdom  than  in  the  loyal  States  ? 

161.  The  products  of  Great  Britain  and  Ireland  in  1863, 
amounted  to  83340200000,  and  in  the  Loyal  States  to  83720- 
000000.  How  much  more  was  the  value  of  the  annual  pro- 
ducts to  each  person  in  the  loyal  States  than  in  Great  Britain 
and  Ireland  ? 


40  ARITHMETICAL    EXAMPLES. 

102.  Suppose  two  locomotives  start  from  the  same  place 
and  move  in  the  same  direction,  the  first  at  the  rate  of  30 
miles  an  hour,  and  the  second  20  miles  ;  after  the  first  has 
gone  150  miles  it  commences  a  backward  movement  with  the 
same  velocity  till  it  m.eets  the  second  engme.  How  fav  from 
the  pohit  of  starting,  and  in  how  many  hours  do  they  meof? 

1G3.  The  Internal  Revenue  collected  upon  advertisements 
in  1SG3,  at  the  rate  of  3  cents  upon  a  dollar,  amounted  to 
*  rit?4062D.     "What  v/as  paid  for  advertising  during  the  year  ? 

104.  V/hat  number  is  that  which  being  divided  by  72,  the 
quotient  increased  by  25,  the  sutn  diminished  by  the  differ- 
ence between  25  and  18,  the  remainder  multiplied  by  T,  and 
the  product  increased  by  (9  x  8)  -=-(3  x  4)  the  sum  will  be  107? 

105.  In  Dec.  1802,  the  United  States  Navy  numbered  427 
vessels,  carrying  3208  guns,  tonnage  340030 ;  in  Dec,  1803, 
there  were  588  vessels,  carrying  4443  guns,  tonnage,  407907. 
What  was  the  increase  in  vessels,  guns  and*  tonnage "? 

100.  How  many  subjects  are  claimed  by  the  British 
government,  there  being  29458442  in  Europe,  4490741  in 
America,  1020525  in  Africa,  173738800  in  Asia,  and^3423- 
990  in  Australia  1 

107.  In  1802  New  Hampshire  reported  2352  school  dis- 
tricts, and  84672  children  who  attended  school.  Required 
the  average  attendance  in  each  district. 

108.  Bought  25  sheep  for  $50;  how  much  less  per  head 
should  I  have  paid,  had  I  purchased  7  more  sheep  with  the 
same  money  1 

109.  According  to  the  census  of  1860,  the  population  of 
Maine  was  628279 ;  New  Hampshire,  326073 ;  Vermont, 
315098;  Massachusetts,  1231006;  Connecticut,  400147; 
Rhode  Island,  174020 ;  New  York,  3880735.  How  many 
more  inhabitants  in  New  York  than  in  New  England  ? 

170.  A  and  B  pay  1.2.25  for  a  barrel  of  apples,  and  20 
cents  for  the  barrel ;  A  contributes  $1.25  and  B  the  remain- 


ARITHMETICAL    EXAMPLES.  41 

der.     They  divide  the  apples  equally,  and  A  takes  the  barrel . 
Which  owes  the  other,  and  how  much  ? 

171.  How  many  melodeons  at  860^  are  worth  as  much  as 
4  pianos  at  8333^  1 

172.  It  is  estimated  that  the  public  lands  of  the  United 
States  amount  to  2235625  square  miles ;  if  cne-haif  of  thi^ 
was  donated  to  various  purposes,  and  the  remanider  waa 
sold  at  ^1.25  per  acre,  what  v/ould  be  the  net  income  ? 

173.  It  is  estimated  that  the  annual  loss  to  the  United 
States  by  intemperance  is  198400000.  Plow  many  school 
houses  could  be  built,  and  schools  sustained  each  year  with 
this  sum,  provided  that  the  cost  of  a  school  house  and  the 
yearly  expenses  of  the  school,  were  each  81200 1 

174.  At  a  certain  election  5000  votes  were  cast  for  three 
candidates.  A,  B  and  C.  B  had  400  more  than  A,  and  C  300 
more  than  B.     How  many  votes  did  A  receive  1 

175.  The  income  from  'the  various  shops  in  Wethersfield 
State  Prison  for  the  year  1803,  was  $13020.80,  the  expendi- 
tures, $12065.30.     Yv^hat  was  the  net  income  ? 

176.  The  number  of  vessels  belonging  to  the  U.  S.  Navy 
which  were  captured  by  the  rebels  during  1863  was  12,  car- 
rying 48  guns,  tonnage,  5947 ;  the  number  destroyed  to  pre- 
vent falling  into  the  enemy's  hands  \vas  3,  carrying  29  guns, 
tonnage  2983 ;  sunk  in  battle,  4,  v.'lth  28  guns*,  tonnage  2201 ; 
lost  by  shipwreck,  13,  with  Gl  guns,  tonnage  4854.  Required 
the  total  naval  loss  during  the  year. 

177.The  revenue  collected  from  railroads  is  3  cents  for  every 
dollar  of  fare ;  from  this  source  $1029288  revenue  was  collected 
in  1863.     What  amiount  was  received  for  passengers'  fare? 

178.  lii  Ehode  Island  there  are  400  school  districts,  and 
29600  children  attend  schools.  Required  the  average  atten- 
dance in  each  district. 

179.  One-half  the  sum  of  two  numbers  is  500,  and  one-half 
their  difference  is  300.     What  are  the  numbers'? 


42  ARITHMETICAL    EXAMPLES. 

180.  The  whole  number  of  pupils  attending  the  four  normal 
schools  of  Massachusetts  in  1802,  and  the  expenses  of  the 
schools  were  as  follows:  Frammgham,  104  pupils,  expenses, 
$3519 ;  Salem,  140  pupils,  expenses,  $4020 ;  Westfield,  179 
pupils,  expenses,  13119;  and  Bridgewater,  141  pupils,  expen- 
ses, ^53977.     AVhat  was  the  average  expense  per  scholar  ? 

181.  The  condition  of  the  banks  of  New  York  city,  April 
16,  1864,  was  as  follows:  Loans,  C^198703699;  specie, 
$2168760;  circulation,  $5779650;  and  deposits,  1168350790. 
How  much  were  the  assets  in  excess  of  the  liabilities  1 

182.  During  the  year  ending  June  80,  1862,  the  number 
of  letters  exchanged  between  the  United  States  and  Great 
Britain  was  1485970  received,  1391S8G -sent;  between  the 
United  States  and  France,  403275  received.  506461  sent. 
How  many  letters  did  the  exchange  with  Great  Britain  exceed 
the  exchange  w^ith  France  ? 

183.  The  postage  on  mails  sent  to  Europe  in  1862  amount- 
ed to  $573533.45;  on  mails  received,  $570562.37.  The 
postage  collected  m  Europe  was  $465744.23,  and  the  remain- 
der w^tS  collected  in  the  United  States.  How  much  more 
was  collected  in  the  United  States  than  in  Europe  ?      ' 

184.  The  postage  on  mails  tranfjported  by  the  Cunard  line 
in  1862  amounted  to  $521854.78.  A¥hat  was  the  amount  of 
postage  on  mails  carried  by  other  lines,  the  whole  amount 
being  as  stated  in  Example  183  ? 

185.  There  were  in  the  State  of  New  York  in  1862,  11750 
public  schools,  attended  by  893000  pupils.  Required  the 
average  attendance  in  each  school. 

186.  In  1862  there  were  554  stone  school  houses  in  the 
State  of  New  York,  964  brick,  10004  frame,  and  a  number 
of  log  school  houses,  making  the  whole  number  11750.  How 
many  less  than  one-fiftieth  of  the  school  houses  were  built  of 
logsl 

187.  ]n  1862  there  were  21145212  acres  of  land  in  Ken- 
tucky, valued  at  $174187933.     How  mach  had  the  land  de- 


ARITHMETICAL    EXAMPLES.  43 

creased  in  value  per  acre  since  18G1,  when  the  average  value 
was  $10,341 

188.  Wisconsin  sent  into  the  army  before  Nov.  1,  1863, 
34  infantry  regiments,  averaging  1001  men  each;  3  rej.n- 
ments  cavalry,  averaging  1290;  13  batteries,  averaging  IGl  ; 
one  company  sharpshooters,  numbering  147  ;  and  2441  re- 
cruits for  old  regiments.  The  quota  under  all  calls  up  to  that 
date  was  44661.  How  much  did  the  State  lack  of  filling  its 
quota  1 

189.  Russia  exported  gold  and  silver  coin  and  bullion,  in 
1861,  amounting  to  5790355  roubles.  The  imports  for  the 
same  time  were  7138395  roubles.  How  much  did  the  im- 
ports exceed  the  exports,  one  rouble  being  worth  80  cents  ? 

190.  A  teacher  having  a  school  of  144  ladies  and  128  gen- 
tlemen, divided  it  into  the  largest  possible  equal  classes,  so 
that  each  class  of  ladies  should  number  the  same  as  each 
class  of  gentlemen.     What  was  the  number  of  classes  ? 

191.  Ohio  produced  in  1862,  35442858  pounds  of  butter, 
worth  on  an  average  20  cents  a  pound,  and  20637235  pounds 
of  cheese,  worth  14  cents  a  pound.  What  was  their  aggre- 
gate value? 

192.  A  farmer  sold  34  bushels  of  oats  and  26  bushels  of 
corn  for  $63.10.  He  received  for  the  corn  35  cents  more  per 
bushel  than  for  the  oats.  What  was  the  price  of  each  per 
bushel  ? 

193.  The  value  of  all  the  exports  of  Russia  in  1861,  by 
maritime  commerce,  was  137702143  roubles;  by  overland 
commerce,  30473888  roubles.  The  value  of  the  imports  for 
the  same  year  was,  by  maritime  commerce,  115651243  rou- 
bles ;  by  overland  commerce,  44028013  roubles.  How 
much  did  the  value  of  the  exports  exceed  the  imports,  a  rou- 
ble being  worth  80  cents  ] 

194.  The  number  of  letters  exchano;ed  between  the  United 
States  and  Europe,  in  1862,  was  2644039  sent,  and  2556624 
received,  being  a  decrease  of  945158  from  the  number  re- 


44  AUITHMETICAL   EXAMPLES. 

ported  the  previous  year.     How  many  letters  were  exchanged 
in  1861  ? 

195.  The  Treasurer  of  Vermont  made  the  following  report 
Sept.  1,  1863  :  Balance  in  treasury,  Sept.  1,  1862,  $224250.- 
41  ;  receipts  from  ordinary  sources  during  the  year,  |774- 
327.30  ;  on  account  of  the  war,  $1853874.28.  The  disburse- 
ments were,  for  civil  purposes,  $281666.34 ;  for  war  pur- 
poses, $2358682.69  ;  interest,  $89669.21.  What  balance  did 
the  Treasurer  report  ? 

196.  In  New  York,  in  1863,  77862  men  were  drafted; 
53109  were  exempted,  14073  paid  commutation,  6619  fur- 
nished substitutes,  1504  failed  to  report.  How  many  entered 
the  military  service  1 

197.  Jan.  1,  1863,  Pennsylvania  had  fiirnishod  men  for  the 
war  as  follows  :  20979  3-months  men  ;  Reserve  Corps,  15- 
856;  under  call  of  July  22,  1861,93759;  under  requisition 
of  July  7,  1862,  40383 ;  under  call  of  Aug,  4,  1862,  15100; 
recruits  for  old  regiments,  9259.  The  Adjutant  General, 
allowing  for  enlistments  in  other  States,  reported  the  whole 
number  200336.  How  many  did  he  estimate  enlisted  out  of 
the  State  1  * 

198.  There  v.^ere  47(>203  votes  cast  for  two  candidates  for 
governor  in  Ohio,  in  1863.  The  majority  of  the  successful 
candidate  was  101079.     How  many  votes  were  cast  for  each  % 

199.  A  speculator  had  210  acres  of  land,  which  he  might 
have  sold  at  $220  an  acre,  and  gained  $6300,  but  after  holding 
for  a  time,  he  sold  it  at  a  loss  of  $3150  ;  how  much  per  acre 
did  it  cost  him,  and  for  how  much  per  acre  did  he  sell  it  ? 

2C0.  A  merchant  bought  3  pieces  of  cloth  of  equal  lengths 
at  $5  a  yard  ;  he  gained  $35  on  the  v.'hole  cost,  by  selling  2 
pieces  for  $350  ;  how  many  yards  in  each  piece  ? 


CHAPTEH  III. 

1.  If  5 1  yards  of  calico  cost  $1.17,  how  much  must  be 
paid  for  43^  yards  ? 

2.  Change  y\  of  f|  of  f  |  to  an  equivalent  fraction,  hav- 
irip-  75  for  its  denominator. 

3.  If  cloth  1.875  yards  in  breadth  require  18.75  yards  in 
length  to  make  a  certain  number  of  garments,  how  many 
yards  in  length  will  it  require  if  the  cloth  be  .625  yards  wide  1 

4.  In  a  certain  school  room,  J  of  the  desks  are  occupied ; 
■i  of  the  scholars  study  grammar ;  1  study  physiology ;  ^ 
study  book-keeping ;  and  the  remaining  scholars  are  equally 
divided  into  3  algebra  classes.  ^  of  the  most  advanced  alge- 
bra class  study  geometry,  and  there  are  5  in  the  geometry 
class.  What  is  the  number  of  scholars  in  the  school-room, 
and  how  many  desks  are  unoccupied  ? 

5.  j\  of  a  certain  number  exceeds  -|  of  the  same  by  153. 
What  is  the  number  1 

6.  A  certain  sum  of  money  is  divided  among  4  persons. 
A  has  I ;  B,  i ;  C,  i  ;  and  D  the  remainder,  v/hich  is  $39. 
IIov/  much  more  has  A  than  D1 

7.  A  book  publisher  sold  2  dozen  Webster's  Unabridged 
Dictionary  at  $60  a  dozen,  15  dozen  Robinson's  Arithmetio 
at  $9,  and  10  dozen  Testaments  at  $2;  the  actual  cost  of  the 
books  was  $250.     How  much  was  his  gain  1 

8.  I  exchanged  14|  cords  of  wood  at  $4^  per  cord,  for 
flour  at  $9 1  per  barrel.     How  much  flour  did  I  receive  ? 

9.  The  product  of  3  numbers  is  112 ;  one  of  them  is  5|; 
another  is  61.     Wliat  is  the  third  1 


46  ARITHMETICAL    EXAMPLES. 

iA    7^-   -I     |of  ^4,x5'    ^       J  of  9| 

10.  Divide  i ^ ^  bv  -I — ^K-* 

fof  2^x3i    ^  j%  of  3 

11.  A  can  do  a  piece  of  work  in  |  of  a  day ;  B  can  do  it 
in  i  of  a  day,  and  C  can  do  it  in  1 J  days.  In  what  time  can 
all  do  it,  working  together  ? 

12.  If  5i  lbs.  of  coffee  cost  $ly^y,what  will  27^  lbs.  cost? 

13.  A  merchant  had  I'OOOO  with  which  to  purchase  goods. 
He  bought  20  pieces  of  sheeting,  each  containing  44  yds.,  at 
$.12  per  yard;  400  pieces  of  calico  of  31  yds.  each,  at  1.17^ 
per  yard  ;  25  pieces  of  cassimere,  each  containing  38.75  yds., 
at  $2,375  per  yard  ;  100  pieces  of  silk,  each  containing  29| 
vds.,  at  $.95  a  yard.     How  much  money  had  he  left? 

14.  In  1S64  Illinois  packed  1273400  hogs,  of  an  average 
weight  of  200  pounds.  How  many  car-loads  would  these 
make,  10  tons  of  2000  pounds  each  loading  a  car? 

15.  How  long  a  train  would  all  the  cars  necessary  to  ship 
the  pork  mentioned  in  the  preceding  example  make,  allowing 
25  feet  for  each  car,  there  being  5280  feet  in  one  mile  ? 

IG.  A  and  B  engage  in  trade.  A  famished  y'y  of  the  cap- 
ital, and  B  j%.  If  B  should  transfer  $379 ;]  of  his  capita^to  A, 
their  shares  would  be  equal.     How  much  did  each  furnish? 

17.  How  many  times  can  a  vessel  containing  {  of  a  gallon 
be  filled  from  |  of  a  barrel  containing  311  gallons? 

18.  Add  the  following  fractions :  i  of  f ,  21,  |  of  |  of  5, 
I  of  -5  of  31. 

19.  Bought  a  cord  of  wood  for  $4,625,  a  cheese  for  $7.- 
5G1,  and  14^^^  lbs.  butter  at  $.25  per  lb.  What  was  the  cost 
of  the  w"hole? 

20.  A  man  purchased  a  number  of  lemons  at  2  cents  each, 
and  I  as  many  at  3  cents  each ;  he  sold  them  all  at  the  rate 
of  2  for  5  cents,  and  gained  25  cents.  How  many  of  each 
kind  did  he  purchase  ? 

21.  A  can  do  a  piece  of  work  in  2|  days,  B  can  do  it  in 
3 1  days.     In  what  time  can  both,  working  together,  do  it? 


ARITHMETICAL    EXAMPLES.  47 

22.  What  number  is  that  from  which,  if  7^  be  taken,  the 
remainder  will  be  9|  ? 

23.  Find  the  sum  of  forty-nine  and  three-tenths,  four  hun- 
dred, and  three  millionths,  subtract  from  it  two  hundred 
forty-six,  and  three  thousandths,  multiply  the  remainder  by 
five  thousand,  and  divide  the  product  by  four  ten-thousandths. 

24.  In  New  Jersey  137578  children  attended  the  public 
schools  in  1861,  and  the  total  expenditures  for  school  purpo- 
ses were  $510283 ;  in  1862,  132590  children  were  in  the 
public  schools,  at  an  expense  of  1562259.  How  much  more 
was  the  expense  per  scholar  the  latter  year  than  the  former  1 

25.  Peter  can  do  a  piece  of  work  in  1|  days,  Martin  in  j^^ 
of  a  day,  and  Jacob  in  2  days,  ffhey  commence  the  work 
together,  but  Martin  ceases  to  labor  after  working  ^  of  a  day, 
and  Jacob  quits  after  having  performed  J  of  the  task,  v/hen 
Peter  completes  the  work.     How  long  does  Peter  work  ? 

23.  If  3  horses  eat  2^  bushels  of  oats  in  2  days,  how 
many  horses  will  eat  34"|  bushels  in  8  days  1 

27.  From  one  take  two  ten-millionths, 

91  X  ^ 

28.  Pteduce  —"FTsf  ^^  ^  decimal  fraction. 

f  of '^i 

29.  In  the  Massachusetts  State  Prison,  for  one  year,  $30958 
was  paid  for  salaries,  $18468  for  provisions,  $7489  for  cloth- 
ing, and  $26432  for  miscellaneous  purposes ;  $53655  was 
received  for  the  labor  of  the  convicts.  How  much  were  the 
net  expenses  of  the  prison  ? 

30.  If  a  family  of  9  persons  consume  98^'^  lbs.  butter  in 
41  v.'eeks,  how  many  pounds  will  each  person  consume  per 
week  ? 

31.  If  I  of  a  bushel  of  corn  be  worth  ^  of  a  bushel  of 
wheat,  and  wheat  be  worth  $1.40  a.  bushel,  how  many  bushels 
of  corn  will  $27  buy  ? 

32.  After  spending  i,  |  of  -f ,  and  j\  of  my  money,  I  had 
$48^  left.     How  much  had  I  at  first  1 


48  ARITHMETICAL    EXAMPLES. 

33.  "VAHiat  is  the  continued  product  of 

9        174A     44f     40.8- 


_,       1961     161      36A  •' 

34.  What  number  is  that  from  which,  if  11  be  subtracted, 
f  of  the  remainder  will  be  42  ? 

85.  How  many  yards  of  carpeting  li  yds.  wide  would  be 
required  to  carpet  a  room  6|  yds.  long  and  5|  yds.  wide? 

36.  Bought  12  yds.  of  cloth  at  $.371  per  yard,  and  agreed 
to  pay  1  of  the  cost  in  butter,  at  $.16|  per  pound  ;  }  in 
money,  and  the  remainder  in  eggs,  at  $.12i  per  dozen.  How 
many  pounds  of  butter  and  dozens  of  eggs  were  required? 

37.  If  21.65  tons  of  hay  are  sold  for  $10821,  what  will  1 
ton  cost  ?  * 

38.  What  will  42.875  yards  of  cloth  cost  at  |5i  per  yard  ? 

39.  What  is  the  profit  upon  one  million  spelling  books,  at 
$.006  per  book  ? 

40.  If  f\  of  a  tub  of  butter  cost  $3.55,  what  will  9  tubs 
cost  ? 

41.  Samuel  Smith  has  99,875  acres  of  land  in  one  field, 
163.625  acres  in  another,  and  243.1678  acres  in  a'third. 
How  much  land  must  he  purchase  to  have  640  acres  ? 

42.  A  farmer  sold  at  one  time  7  tons  and  375  thousandths 
of  a  ton  of  hay,  at  another  time  12  tons  and  3125  ten-thou- 
sandths of  a  ton,  and  at  a  third  time  13  tons  and  3125  hun- 
dred-thousandths of  a  ton,  at  an  average  price  of  $8  per  ton. 
How  much  did  he  receive  for  the  whole  ? 

43.  What  is  the  sum  of  2}  decimal  units  of  the  first  order, 
4f  of  the  second  order,  7 ^\  of  the  .third  order,  and  O^^  of 
the  fourth  order  ? 

44.  How  many  pairs  of  pants  can  be  m.ade  from  48.6  yds. 
of  cloth,  allowing  1.8  yds  per  pair? 

45.  I  purchased  a  quantity  of  grain,  f  of  it  being  oats,  at 
$.75  a  bushel ;  j\  wheat,  at  $1.50  a  bushel,  and  the  remain- 


ARITHMETICAL    EXAMPLES.  49 

der  barley,  at  $.90  a  bushel,  to  the  amount  of  $7,425.     How- 
much  did  I  pay  for  the  whole  ? 

46.  A  owns  f  of  a  ship ;  he  sells  |  of  his  share  for  $1800. 
What  is  the  value  of  the  ship  ? 

47.  A  can  perform  a  piece  of  work  in  9  days ;  A  and  B 
together  can  do  the  same  in  G  days ;  A,  B  and  C  working  to. 
gether  can  do  it  in  4  days.  In  how  many  days  can  B  and  C, 
working  together,  perform  the  whole  ? 

48.  What  is  the  sum  of  5/^  decimal  units  of  the  first 
order,  63^0  of  the  second  order,  7y^g  of  the  third  order,  8f  of 
the  fourth  order,  9^  of  the  fifth  order,  and  3^  of  the  sixth 
order  ? 

49.  Multiply  the  sum  of  the  quotients  of  270-^4000 ; 
1307^.008:  .0103-^.04;  70.303^.5;  3.78-^200;  .04735 
-^.0005;  30-^.004;  903-^30000  by  25.25. 

50.  There  are  two  numbers  w^hose  sum  is  1:^\,  and  whose 
difference  is  ^\.     What  are  the  numbers  ? 

51.  A,  B  and  C  own  a  furnace ;  A  owns  fj\  of  it ;  B  owns 
^3-  of  it  more  than  C.  What  parts  of  the  furnace  do  B  and 
C  own  respectively  ? 

52.  X  and  Y  traded  in  company.  X  put  in  merchandise 
valued  at  $8000,  and  Y  put  in  $20000  cash.  They  agreed  to 
share  the  gains  or  losses  equally.  At  the  end  of  two  years, 
the  business  proving  unsuccessful,  they  dissolved  partnership, 
and  found  the  losses  amounted  to  $11500.  What  was  each 
partner's  share  of  the  remaining  property  ? 

53.  In  the  thirty-eighth  Congress,  1834,  the  House  of  Rep- 
resentatives was  divided  into  two  parties,  so  that  f  of  the 
number  in  one  was  equal  to  ||  the  number  in  the  other,  and 
there  were  177  members.  Required  the  number  of  each 
party. 

54.  What  is  the  sum  of  the  continued  products  of  f  x  4|  x 

21 

f  X  I  X  /-  and  3|  X I  X  ^  ^ 


50  ARITHMETICAL    EXAMPLES. 

55.  A  man  having  ^OQ,  gave  A  $5  more  than  J  of  the 
whole;  B  $2  less  than  J  of  the  remamder;  C  ^12  more  than 
^  of  the  remainder,  and  the  rest  he  gave  to  D.  Uow  much 
did  each  receive  I 

50.  The  traneactions  of  the  Treasury  of  the  State  of  New 
York,  in  1SG3,  were  as  follows :  Balance  in  Treasury  at  the 
be'irinning  of  the  year,  $5750621.19;  receipts  during  the  year, 
818656285.17  ;  payments,  $20703585.84.  How  much  less 
ill  Treasury,  Jan.  1,  1864,  than  Jan.  1,  1863? 

57.  Multiply  1  of -j\  of  11  by  -%  of  if  of  ^|. 

58.  A  teacher  spends  |  of  his  salary  in  board  for  himself 
and  family,  j\  in  clothnig  himself,  his  wife's  clothing  costs  | 
as  much  as  his  own,  his  daughter's,  \  as  much  as  his  wife's; 
his  son's,  i  as  much  as  his  daughter's,  and  he  lays  by  $115. 
What  is  his  salary  1 

59.  The  marble  used  in  the  Capitol  extension,  AVashington, 
had  cost,  Jan.  1,  1863,  $1029041,  and  the  cutting  and  the  set- 
ting of  the  same,  $1373749  more;  19403800  bricks  had  been 
used,  worth  $7.50  per  thousand,  and  the  new  iron  dome  cost 
$900000.     Eequired  the  sum  of  these  expenditures. 

60.  Divide  172170063  by  .0000009. 

61.  What  will  15  [-1  doz.  eggs  cost  at  18^  cents  per  doz.  1 

62.  Add  nine  ten-thousandths,  1000  and  six-millionths,  3 
and  forty -seven  ten  mill  ionths,  246  and  twenty-five-thousandths. 

63.  John  Brown  killed  an  ox,  which,  when  dressed,  weighed 
11781  lbs.,  he  kept  |  of  it  for  his  own  use,  and  sold  |  of  the 
remainder  to  Hiram  Jones.  What  was  the  value  of  the  re- 
mainder at  1 1 1  cents  per  pound  ? 

64.  A  merchant  purchased  17  bales  of  cotton  goods  con- 
taining 587^  y<^ls.,  at  8]  cents  per  yard;  he  sold  I  of  it  at  11 1 
cts.  per  yard,  and  |  of  the  remainder  at  12^  cts.  per  yard. 
How  much  would  he  receive  for  what  still  remained  at  13 
cents  per  yard  and  what  profit  would  the  merchant  make  on 
his  bargain  1 


AIUTHMETiOAL    EXAMPLES.  51 

05.  Fanny  Church  disposed  of  838.88f  as  follows:  She 
gave  ^  of  it  to  the  Siinitary  Commission,  f  of  the  remainder 
to  the  Christian  Commi^ision,  and  the  remainder  she  divided 
equally  among  7  poor  v/omen.  How  much  did  each  woman 
receive  1 

GO.  What  number  must  be  multiplied  by  9^  x  3^,  that  the 
product  may  be  1001 

.07.  A  boy  in  flying  his  kite  lost  |  of  the  string,  then  added 
05  feet  and  found  that  it  was  just  f  of  the  original  length. 
What  was  the  length  at  first  ? 

08.  A  and  B,  being  133  miles  apart,  travel  towards  each 
other,  both  starting  at  the  same  time.  They  meet  at  the  end 
of  10  hours,  and  find  that  A  has  traveled  1^  miles  more  than 
B  each  hour.     How  many  miles  did  each  travel  ? 

09.  California  cultivated,  in  1801,  301350  acres  of  wheat, 
which  produced  8810940  bushels,  and  20780  acres  of  potatoes, 
from  which  12DS750  bushels  were  harvested.  Allowing  the 
expense  of  cultivating  an  acre  of  each  to  be  the  same,  the 
wheat  worth  $1.75  per  bushel,  and  the  potatoes  8.00,  how 
much  more  profitable  per  acre  was  the  wheat  than  the  potato 
crop  1 

70.  A  barrel  holding  3H  gallons  is  a  fall ;  9|-  gallons  being 
drawn  ofiT,  what  part  of  the  contents  remain  ? 

71.  Reduce  to  their  lowest  terms  Iff f|  ;  |f};  ||-^^,  and 

13  3  9 

3  7  04* 

72.  Three  men.  A,  B  and  C,  start  from  the  same  point  to 
travel  around  an  island  100  miles  in  circumference  ;  A  travels 
22|  miles  each  day;  B,  llf  miles,  and  C,  12||  miles.  Re- 
quired the  least  number  of  days  in  which  all  vrill  be  together 
ac  tlic  point  of  starting,  and  how  many  times  each  will  have 
trciveled  around  the  island. 

73.  If  at  each  stroke  of  the  piston  rod  of  a  locomotive 
engine  a  distance  of  15.025  feet  be  passed  over,  how  many 
strokes  must  be  made  in  passing  from  New  York  to  Washing- 


52  AKITHMETICAL    EXAMPLES. 

ton,  the  distance  being  225.25.  miles,  allowing  5280  feet  in 
each  mile  ? 

74.  If  the  circumference  of  the  truck  wheels  of  an  engine 
he  8.8  feet,  and  of  the  drivers  21.3  feet,  how  many  more  times 
wiil  the  one  revolve  than  the  other,  in  running  from  New 
York  to  Albany,  the  distance  being  150  miles? 

75.  The  enumeration  of  youths  of  school  age  in  Ohio  in 
1857  was  838037;  the  enrollment  of  those  in  attendance  was 
G03347,  and  the  average  attendance,  350867.  In  1862  the 
enumeration  was  920890;  enrollment,  723669,  and  average 
attendance,  433343.  Required  the  respective  increase  in 
enumeration,  enrollment  and  average  attendance. 

76.  If  I  of  §  of  an  acre  of  land  sell  for  $16//,),  what  is  5 
times  i  of  i-^-  of  an  acre  worth  at  the  same  rate? 

77.  S.  Smith  being  asked  how  many  sheep  he  had,  replied 
that  he  had  them  in  4  fields  ;  in  the  first  there  were  5  less 
than  i  of  the  whole  number  of  sheep ;  in  the  second  i  as 
many  as  in  the  first ;  in  the  third  |  as  many  ;  and  in  the  fourth 
there  were  30  sheep.     How  many  sheep  had  he  ? 

78.  A  man  spent  $18.81  for  equal  quantities  of  butter  and 
lard;  for  the  butter  he  paid  8.18  per  lb.,  and  for  the  lard, 
$.15  per  lb.     How  much  of  each  did  he  buy  ? 

79.  A  had  $576,  which  was  $156  more  than  |  of  2^  times 
B's  money.     How  much  money  had  B  ? 

80.  If  i  of  John's  marbles  equals  j  of  James',  and  both  to- 
gether have  44  ;  how  many  marbles  has  each  ? 

81.  If  one  yard  of  sheeting  cost  18^  cents,  how  many  yards 
may  be  bought  for  $1.31 1  ? 

82.  The  State  of  Kansas  paid  $14009.67  for  teachers'  sala- 
ries in  1862,  and  $1747.23  for  incidentals.  The  district  taxes 
amounted  to  $10381 .81,  and  the  school  fund,  $4148.45.  Hov/ 
large  a  school  debt  remained  to  be  provided  for  the  next 
year  ? 

83.  It  is  llOj^i-  miles  from  New  York  to  Hudson,  and  74  }| 


ARITHMETICAL    EXAMPLES.         '  53 

miles  from  New  York  to  Poughkeepsie ;  how  many  miles  from 
Poiighkeepsie  to  Hudson  ? 

84.  41 1  is  the  f  part  of  what  number? 

85.  A  owns  j\  of  a  cargo  worth  $23426^ ;  B  owns  f  of  a 
steamboat  worth  ^17425^^.  They  exchange  stocks.  How 
much   money  must  A  pay  to  B  ? 

"!  86.  A  father  divided  $3000  among  his  0  sons  so  that  each 
elder  brother  had  $100  more  than  his  next  younger  brother. 
Required  the  share  of  the  youngest. 

87.  Bought  S3  baskets  of  peaches,  each  basket  containing 
^  of  a  bushel,  at  ^l.o7|-  per  bushel.     What  was  the  cost? 

88.  From  23|  bushels,  subtract  the  sum  of  |  and  4f  bushels. 

89.  If  a  man  earns  856  in  j\  of  a  month,  how  much  does 
he  earn  in  one  week,  allowing  4  weeks  to  a  month  ? 

90.  A  merchant  in  selling  10|  lbs.  sugar  at  the  rate  of  8 
lbs.  for  $1,  gains  17  cents;  what  was  the  cost  of  the  sugar  per 
pound. 

91.  When  potatoes  are  worth  $.87^  per  bushel,  and  corn 
$1.16*-,  how  many  bushels  of  corn  will  a  farmer  receive  in 
exchange  for  28  bushels  of  potatoes  ? 

92.  If  9  horses  eat  |  of  7}  bushels  of  oats  in  a  day,  how 
much  does  each  horse  eat  ? 

93.  Bought  1  of  3{|  cords  of  wood  for  f  of  $17^.  How 
much  did  one  cord  cost  ? 

94.  If  1.75  acres  produce  6.51  tons  of  hay,  how  many  tons 
will  7.625  acres  produce? 

95.  A  man  bought  43f  yds.  of  carpeting  for  $58^ ;  he  sold 
I  of  the  piece,  gaining  |.16|  on  each  yard  sold.  How  much 
did  he  receive  for  it? 

90.  If  28  men  build  a  bridge  in  4f  days,  how  many  men 
could  build  the  same  in  2|  days  ? 
72_4i      72 

97.  Reduce  7-^-^^  x  ktA  to  its  simplest  form. 
|of3|     31f 


54  ARITHMETICAL   EXAMPLES. 

98.  The  distance  from  Boston  to  Worcester  is  44  miles; 
A,  starting  from  Boston,  travels  j\  of  the  distance ;  B,  start- 
ing from  Worcester,  travels  -fj  of  the  distance  in  the  same 
time.     How  far  apart  are  they  1 

99.  A  merchant  has  3  pieces  of  cloth,  containing  respec- 
tively 28f  yds.,  35i  yds.  and  41  f  yds.;  after  selling  several 
yards  from  each  piece,  he  finds  he  has  left  in  the  3  pieces 
65f  yds.     How  many  yards  has  he  sold  ? 

100.  What  number  is  that  to  which,  if  you  add  ^  of  /p  of 
itself,  I  of  the  sum  will  be  101  ? 

101.  Bought  2.125  yards  of  cloth,  1.375  yards  wide,  for 
$4,675;  what  will  27.625  yards,  IJ  yards  wide,  cost,  at  th^ 
same  price  per  square  yard  ? 

102.  A  and  B  traded  with  equal  sums  of  money  ;  A  gained 
a  sum  equal  to  ^  of  his  stock ;  B  lost  §220,  and  then  had  ^ 
as  much  as  A.     What  was  the  original  stock  of  each  ? 

103.  James  can  do  a  piece  of  work  in  -f  of  a  day  ;  Henry 
can  do  it  in  1\  days,  and  John  can  do  it  in  |  of  a  day.  How 
much  longer  will  it  take  John  to  do  the  work  alone  than  it 
does  James  and  Henry  working  together  ? 

104.  From  a  piece  of  calico  containing  33|-  yds.  there  have 
been  sold,  at  different  times,  llf  yds.,  7f  yds.,  2^\  yds.  and 
H  yds.     How  many  yards  remain  1 

2  3 

105.  What  number  must  be  multiplied  by  ^,  that  the 
product  may  equal  1  ? 

106.  The  report  from  the  Army  of  the  Potomac,  Feb.  1, 
1862,  was  as  follows:  There  were  present  for  duty  1002  men 
less  than  -f  of  the  whole  army ;  1621  men  less  than  j\  were 
in  hospitals;  107  less  than  ^j  were  in  confinement;  124 
more  than  /g  w^re  on  furlough,  and  1580  were  unaccounted 
for.  How  many  men  were  reported  for  duty,  in  hospital,  in 
confinement,  and  on  furlough,  respectively,  and  what  was  the 
aggregate  strength  of  the  army '? 


ARITHMETICAL    EXAMPLES.  55 

107.  If  j\  of  a  yard  cost  §10,  what  quantity  •will  |17i 
purchase  ? 

lOS.  A  merchant  sold  a  piece  of  cloth  for  ^>.24,  and  therehy 
lost  i  of  his  purchase  money.  ^Yhat  part  of  his  purchase 
money  would  he  have  gained  had  he  sold  it  for  |34  ? 

109.  George  Hawkins  leased  100  acres  of  land  in  Missis- 
sippi, of  the  U.  S.  Government,  for  one  year ;  his  cotton  crop, 
raised  upon  f  of  the  land,  averaged  1  bale  of  400  lbs.  per 
acre;  he  planted  corn  upon  the  remaining  land,  raising  45| 
bushels  per  acre.  He  sold  the  cotton  at  50  cents  per  pound, 
and  the  corn  at  75  cents  per  bushel ;  his  expenses  for  farming 
implements,  labor,  and  Government  tax,  were  just  .}  the  gross 
receipts.     What  were  the  net  profits  for  the  year  1 

110.  Bought  a  horse  and  saddle  for  $150,  and  paid  for  a 
tiigcry  I  of  what  I  paid  for  the  horse ;  the  saddle  cost  f  the 
value  of  the  horse.     What  was  the  price  of  each  ? 

111.  A  company,  whose  capital  stock  is  divided  into  1000 
equal  shares,  consolidate  the  stock  into  800  equal  shares. 
How  much  larger  would  a  share  of  the  latter  be  than  one  of 
the  former  size  1 

112.  If  22  boarders  consume  a  barrel  of  beef  in  63  days, 
how  long  would  it  last  if  G  more  w^ere  added  to  their  number '? 

113.  If  a  man,  by  laboring  14  hours  a  day,  can  perform  a 
certain  piece  of  work  in  G  days,  how  many  days  would  it  re- 
quire to  do  the  same  w^ork,  by  laboring  12  hours  a  day  ? 

114.  In  185G,  405G471  votes  were -cast  for  three  presiden- 
tial candidates.  Buchanan  received  497573  votes  more,  and 
nilmore  467309  votes  less,  than  Fremont.  How  many  voles 
did  each  receive  ? 

115.  If  a  horse  eat  19f  bushels  of  oats  in  87f  days,  hov^ 
many  bushels  would  14  horses  eat  in  30  days  1 

IIG.  James  Stow  can  mow  a  field  in  6  days,  by  working 
10  hours  a  day ;  his  son  George  can  mow  the  same  field  in  9 
days,  by  working  8  hours  a  day.     How  long  will  it  take  them 


56  ARITHMETICAL    EXAMPLES. 

both  to   mow  the  field,  provided  they  each  work  6  hours 
a  day  ? 

117.  An  Illinois  farmer  sold  2r2f  bushels  of  wheat  for 
12013  .  ^28^2  bushels  of  corn  for  $178f  ;  187y\  bushels  of 
oats  for  '184^.  How  many  bushels  of  grain  did  he  sell,  and 
how  much  did-  he  receive  for  the  whole  ? 

118.  Tiie  total  expenses  of  public  schools  in  Pennsylvania, 
in  1862,  were  $1955315,  and  0&54G3  scholars  attended  school. 
The  same  year  there  were  G8954  scholars  in  ihe  public  schools 
of  Philadelphia,  educated  at  an  expense  of  $604100.  How 
much  were  the  expenses  per  scholar  in  the  city  more  than  in 
the  State  at  large  1 

119.  Bought  I  of  a  ten-acre  lot,  and  sold  4  of  what  I  pur- 
chased.    How  much  did  I  sell  ? 

120.  Bought  8  lbs.  hyson  tea  and  12  lbs.  black  tea.  Tlie 
price  per  pound  of  the  latter  v/as  |  the  price  of  the  former, 
which  was  ly^'^.     What  did  the  whole  cost? 

121.  What  is  the  difference  between  -"*  p-  yards,  and  159 
whole  yards '? 

122.  A  lady  spent  ^  of  the  day  in  sleep,  ^  in  visiting,  J-  at 
her  toilet,  ^  in  reading,  .and  2  hours  each  day  in  receiving 
calls.     How  much  of  her  time  remained  for  other  occupations  1 

123.  A  gentleman  bequeathed  }j  of  his  estate  to  his  '>vife,  { 
of  the  remainder  to  his  oldest  son,  and  |  of  the  residue  to  his 
oldest  daughter,  whose  share  was  |'C)84.G6|.  What  was  the 
value  of  the  estate  ? 

124.  The  estimated  value  of  all  the  gold  throughout  the 
world  in  1863,  was  $4860000000;  of  the  silver,  $5700000000. 
Yf  hat  part  of  this  sum  was  produced  the  same  year,  the  annual 
product  of  gold  being  $180000000,  and  of  silver,  $600000001 

125.  A  having  104^  bushels  of  wheat,  sold  ^  of  it  to  B, 
who  sold  I  of  what  he  bought  to  C,  who  sold  }  of  what  he 
bought  to  D.     How  many  bushels  did  each  purchase  1 

126.  A  boy  can  do  a  certain  piece  of  work  in  3|  days,  and 


ARITHMETICAL    EXAMrLES.  57 

a  man  can  do  the  same  in  -f  of  the  time.     IIow  many  days 
will  both  working  together  require  to  do  the  v/ork  ? 

/127.  A  grocer  has  74  J- 1  gallons  of  beer,  which  he  wishes  to 
put  into  Lotties,  each  holding  j\  of  a  gallon.  How  many 
dozen  bottles  must  he  obtain '? 

128.  A  garrison  of  5000  men  were  besieged  in  a  town, 
with  provisions  for  three  w-eeks,  allow^ing  each  man  16  ounces 
per  day.  Being  reinforced  by  3000  men,  upon  what  allow- 
ance per  day  must  the  garrison  be  put,  that  the  same  provi- 
sions may  last  four  weeks  1 

129.  What  will  12.75  bales  of  cotton  cost,  each  bale  weigh- 
ing 7.75  cwt.,  at  $28,625  per  cwt.  1 

ISO.  What  is  the  greatest  common  divisor  of  408,  1190 
1445  and  4012? 

131.  How  many  limes  does  the  sum  of  21]  and  12'  co  - 
tain  their  difference  1 

132.  In  a  certain  school,  .375  of  the  pupils  study  arithm  > 
tic,  .3  study  grammar,  .25  study  geography,  and  the  remai.;, 
der,  w^hich  is  21,  learn  to  read.  What  is  the  whole  numba 
of  pupils  1 

133.  The  public  debt  of  Austria  in  1863  was  2539090836 
florins,  and  her  population  was  34714326.  What  was  the 
debt  per  capita,  a  florin  being  worth  iO  cents  in  United  States 
money  ? 

134.  Divide  $1000  among  7  boys  and  9  girls,  giving  to 
each  girl  i  as  much  as  to  each  boy.  How  much  does  each 
boy  and  girl  respectively  receive  ? 

135.  If  7  men  or  11  boys  can  perform  a  piece  of  work  in 
28  days,  in  what  lime  can  11  men  and  7  boys  do  the  same  ? 

136.  Four  persons  bought  a  house  together  for  $8250  ;  B 
paid  twice  as  much  as  A,  C  paid  as  much  as  A  and  B,  and  D 
paid  as  much  as  A  and  C.     How  much  did  each  pay  ' 

137.  In  Belgium,  the  budget  for  1863  gives  the  total  re- 
ceipts at  155946790  francs,  and  the  expenditures  at  150120345 


58  ARITHMETICAL   EXAMPLES. 

francs.     How  many  more  dollars  were  the  receipts  than  the 
expenditures,  5  francs  being  worth  98  cents  U.  S.  money  1 

138.  A  man,  going  a  journey  of  418  miles,  finds  at  the  end 
of  5  days  that  the  distance  he  has  traveled  is  ^{  of  the  re- 
maining distance.     How  many  miles  does  he  travel  per  day  1 

139.  A  regiment  of  soldiers,  consisting  of  1025  m.en,  is  to 
be  furnished  with  coats,  each  to  contain  2|  yards,  1 1  yards 
wide.  How  many  yards  of  cloth,  |f  yards  wide,  will  line 
them  ? 

140.  How  many  times  is  .75  of  2.625  contained  in  .375 
of  261. 

141.  A  man  having  a  cow  and  horse  found  that  4  loads  of 
hay  would  keep  them  both  6  months;  having  disposed  of  his 
horse  he  found  that  the  same  quantity  of  hay  would  keep  his 
cow  14  months.     In  what  time  did  each  consume  1  load  1 

142.  Bought  a  hogshead  of  molasses  containing  128  gallons 
at  8.65  a  gallon  ;  paid  $.80  for  cartage,  and  lo^t  16  gallons  by 
leakage.  At  what  price  per  gallon  must  the  remainder  be 
sold  to  gain  ^  of  the  entire  cost  1 

143.  Jan.  20th,  1864,  Gen.  B.  F.  Butler  seized  at  NorfoKc, 
Va.,  48  barrels  of  whiskey,  each  containing  31.5  gallons;  this 
was  sold  for  the  U.  S.  Government,  |  at  $7.50  per  gallon,  and 
the  remainder  at  $8.75  per  gallon ;  the  parties  violating  the 
laws  of  trade  were  also  fined  $1000.  How  much  did  the 
Government  receive? 

144.  The  number  of  the  Union  army  killed  in  the  battle  of 
Gettysburg  was  515  more  than  y'^-  of  the  whole  loss;  the 
number  of  wounded  was  956  more  than  4i  times  the  number 
killed  ;  there  were  6647  missing.     What  was  the  whole  loss  ? 

145.  A  boy  bought  a  slnte,  a  book  and  a  pen  for  80  cents; 
the  pen  cost  10  cents,  and  the  book  co?t  If  times  as  much  as 
the  slate  and  pen.     How  much  did  each  cost  1 

146.  Divide  $870  among  A,  B  and  C,  so  that  ^  of  A's 
money  shall  be  equal  to  |  of  B's,  or  |  of  C's. 


ARITHMETICAL    EXAMPLES.  59 

147.  Bouglit  a  horse  for  |115.  At  what  price  must  it  be 
sold  so  that  the  gain  shall  be  |  of  the  cost? 

148.  By  soiling  a  house  for  |2175,  my  gain  was  y\  of  the 
cost  of  the  house.     What  did  I  pay  for  the  house  '? 

149.  A  grocer  bought  a  ca;ik  of  sugar,  containing  400 
pounds,  for  $32 ;  a  part  of  it  being  damaged  he  sold  the  ro- 
inainder  for  f  the  cost  per  pound,  and  thereby  gained  a  sum 
equal  to  J  of  his  purchase  money.  How  many  pounds  wcro 
damaged  ? 

150.  A  merchant  bought  a  b.ng  of  coffee,  containing  80 
pounds,  at  15  cents  per  pound  ;  he  also  paid  8.54  for  roasting 
it.  For  what  must  it  bo  sold  per  pound  to  yield  a  profit  of 
I  the  cost  of  the  coffee,  allov.'ing  to  each  pound  j^j  of  a  pound 
for  waste  ? 

151.  The  entire  population  of  Denmark  and  the  two  Duchies 
of  Holstein  and  Schleswig,  is  2554870;  Denmark  contains  3 
times  as  nmny  inhabitants  as  Holstein — 32706,  and  Schleswig 
contains  134519  less  than  Holstein.  "What  is  the  population 
of  Denmark  and  the  Duchies  respectively  ? 

152.  Bought  a  cask  of  nails  containing  100  pounds  at  4f 
cents  per  pound,  and,  after  reserving  15  pounds  for  myself,  I 
sold  the  remainder  at  5|  cents  per  pound.  How  much  did  I 
gain  1 

153.  A  can  do  I  of  a  piece  of  work  in  4  days ;  B  can  do  } 
of  it  in  5  days ;  C  can  do  i  of  it  in  3  days,  and  D  can  do  } 
of  it  in  11  days.     How  long  will  it  take  them,  all  to  do  it? 

154.  Divide  :^  of -|,-l,yji  of   *^^ 


^^- 


0064  '  .0125       .081 


155.  A  man  owned  £e^■enty-f!ve-t^oueandLhs  of  the  stock 
in  a  bank,  and  sold  three  Iiundred  and  twenty-five  ten-thou- 
sandths of  the  whole  stock.     How  much  did  he  still  own? 

150.  A  mast  stands  4-  in  the  ground,  j  in  the  water,  and  33 
feet  above  the  water.     What  Is  its  length  ? 

157.  I  sold  an  article  for  J  more  than  it  cost  me,  to  A,  vv-hp 


60  ARITHMETICAL    EXAMPLES. 

sold  it  to  B  for  $10,  which  was  i  less  than  it  cost  him.     What 
did  it  cost  me  ? 

158.  The  number  of  postage  stamps  sold  in  one  year  was 
as  follows:  53893792  one-cent  stamps;  151223056  three-cent; 
677200  five  cent;  3925690  ten-cent;  1053900  twelve-cent; 
650600  twenty-four-cent;  340000  thirty-cent;  and  24280 
ninety-cent  stamps.  What  was  the  whole  number  of  stamps 
and  their  value  ? 

159.  Seven  men  engage  to  do  a  piece  of  work  in  a  given 
time,  but  three  of  them  failing  to  come,  the  work  was  pro- 
longed 7:1-  days.  In  what  time  would  the  seven  men  have 
done  it  ? 

1 60.  The  report  of  the  Normal  School  at  Albany,  N.  Y.,  for 
the  year  1863,  showed  that  the  number  of  males  was  1  less 
than  I  of  the  whole  number  in  attendance;  the  number  of  fe- 
males was  32  more  than  |  of  the  whole  number,  and  22  less 
than  4  times  the  number  of  graduates  ;  and  three-fourths  of 
the  entire  number  of  graduates  were  females.  What  was  the 
whole  number  of  graduates,  and  how  many  were  m.ales  ? 

161.  A  mnn  bought  3  barrels  of  molasses,  containing  re- 
spectively 30.375,  33.675,  and  28.6625  gallons,  at  an  average 
price  of  $.375  per  gallon.     What  was  the  whole  cost  ? 

162.  A  person  proposes  to  sell  his  horse  by  lottery;  if  the 
price  of  the  tickets  be  $3  each,  he  will  lose  $20  on  his  horse, 
but  if  he  sell  them  at  $4  each  he  will  gain  $20.  What  was 
the  value  of  the  horse  and  the  number  of  tickets  ? 

163.  There  is  an  island  27  miles  in  circumference;  A,  B 
and  C  start  from  the  same  point,  and  travel  in  the  same  di- 
rection around  it ;  A  goes  at  the  rate  of  4  miles ;  B,  7  miles, 
and  C,  10  miles  per  hour.  In  what  time  will  they  all  be  to- 
gether 1 

164.  What  are  all  the  exact  divisors  of  560 1 

165.  A  person  after  spending  $40  more  than  f  of  his 
money,  had  $60  less  than  -f  of  it  left.  How  much  money  had  he  ? 


ARITHMETICAL    EXAMPLES.  61 

166.  In  1860  Georgia  cultivated  14321  farms  and  planta- 
tions, containing  an  average  of  563  acres  each,  at  an  average 
value  of  $20  per  acre.  New  Jersey  cultivated  18518  farms, 
containing  an  average  of  105  acres  each,  at  an  average  value 
of  $94  per  acre.  Of  how  much  greater  value  were  the  farm- 
ing lands  of  the  latter  State  considered,  than  those  of  the 
former  ? 

IGT.  From  a  cask  of  rum  there  were  drawn  off  26  gallons; 
I  of  the  remainder  leaked  out ;  the  cask  was  then  found  to  be 
4  gallons  more  than  I  full,  How  many  gallons  did  the  cask 
at  first  contain  ? 

168.  A  man  being  asked  his  age,  replied,  "  If  ^  of  my  age 
be  multiplied  by  11,  and  ^  of  it  be  multiplied  by  15,  and  I 
of  it  be  added  to  the  sum  of  these  products,  the  sum  will  be 
381.     What  was  his  age  ? 

169.  The  Illinois  Central  Railroad  sold,  in  one  month, 
16461  acres  construction  land,  at  ^11}  per  acre;  242  acres 
interest  fund  land  at  891-  per  acre;  2781  acres  free  lands  at 
$10f  per  acre ;  and  4  town  lots  at  8425.50  each.  How  much 
were  the  total  receipts  from  the  sale  of  lands  ? 

170.  The  receipts  of  the  same  railroad  for  the  same  month 
were,  from  passengers,  $138615.83 ;  from  freight,  $1^4226.20 ; 
from  mails,  $6358.33 ;  from  rent  of  road,  $4000,  and  from 
other  sources,  $5000.  How  much  did  the  receipts  from  run- 
ning the  road  exceed  those  from  sale  of  lands  1 

171.  A  and  B  have  the  same  income  ;  A  saves  |  of  his,  but 
B  spends  1|  times  as  much  as  A,  and  finds  himself  $98.56  in 
debt  at  the  end  of  the  year.     What  is  their  income  ? 

172.  The  third  satellite  of  Jupiter  is  .0000885  of  the  mass 
of  the  planet,  and  .02947  of  the  mass  of  the  earth.  The  mass 
of  Jupiter  is  how  many  times  that  of  the  earth  1 

173.  If  8|  ounces  of  bread  are  bought  for  $.061,  ^hen 
wheat  is  $li  per  bushel,  how  much  bread  may  be  bought  for 
$.25  when  wheat  is  $|  per  bushel  1 


62  AEITHMETICAL   EXAMPLES. 

174.  What  is  the  sum  of  45  millionths,  45  thousandths,  45 
hundredths,  45  tenths^  and  45  units  ? 

175.  In  1861,  the  revenue  of  the  Post  Office  Department 
was  19049296.40,  from  28586  offices;  in  1862,  it  was  ^10388- 
934.60,  from  199"3  offices.  How  much  more  was  received, 
on  an  average,  from  each  office,  the  latter  year  than  the 
former  1 

176.  A  market  woman  wished  to  sell  a  basket  of  oranges  ; 
her  first  customer  bought  i-  of  what  she  had,  and  gave  her 
back  5  ;  the  second  bought  j  of  what  she  then  had,  and  gave 
her  back  10;  the  third  bought  J-  of  the  remainder,  and  gave 
her  back  15;  the  fourth  bought  |  of  the  residue,  and  gave 
her  back  20 ;  after  which  she  found  she  had  60  oranges  lefc. 
How  many  had  she  at  first  ? 

177.  If  J  of  a  yard  of  cloth  cost  S/j,  what  will  f  of  a  yard 
cost? 

178.  The  exterior  semi-diameter  of  the  exterior  ring  of 
Saturn  is  88209  miles,  and  of  the  interior  ring  75845  miles ; 
the  width  of  the  interval  between  the  rings  is  1791  miles,  and 
the  space  between  the  planet  and  interior  ring  is  19089  miles. 
What  is  the  width  of  the  rings,  the  serai-diameter  of  the  ^ 
planet  being  39580  miles  1 

179.  A  and  B  can  perform  a  piece  of  work  in  1  ^  days;  A 
and  C  in  two  days  ;  C  and  B  in  2|  days.  In  vvhat  time  would 
each  perform  the  work  alone,  and  how  long  would  it  take 
them  to  do  the  work  together  1 

180.  Bought  7640  brick,  at  $4.75  per  1000 ;  26789  feet  of 
lumber,  at  12.75  per  100;  and  986  feet  of  pine  boards,  at 
$20  per  1000;  I  paid  $.35  per  1000  for  planing  23463  feet 
of  boards.     What  was  the  whole  bill  ? 

181.  There  were  193  applications  for  admission  into  the 
Normal  School,  at  Albany,  in  1864 ;  the  number  that  passed 
examination  was  2  less  than  4  times  the  number  that  failed. 
How  many  failed,  and  how  many  were  admitted  1 

182.  A  speculator  gave  119550  for  horses,  and  sold  a  cer- 


ARITHMETICAL   EXAMPLES.  63 

tain  numlDer  of  them  for  680:25,  at  >UO.j  each;  by  so  doing 
he  lost  810  apiece.  For  how  much  must  he  sell  the  remain- 
ing horses  each,  to  gain  84'25  by  the  operation  ? 

183.  A  and  B  together  have  6600  ;  j  of  what  A  ha=:,  added 
to  1  of  wliat  B  has,  amounts  to  8135.     What  have  they  each] 

184.  In  186*2,  the  export  of  petroleum  from  four  ports  was 
as  follows,  viz. :  from  New-York,  6783563  gallons,  valued  at 
S203T413;  from  Philadelphia,  ^eOT^OS  gallons,  worth  85-29- 
575;  from  Boston,  891616  gallons,  worth  8457859;  from 
Baltimore,  1120000  gallons,  worth  8500000.  How  many 
gallons  were  exported,  and  of  what  value  ? 

185.  What  is  the  smallest  sum  of  money  with  which  I  can 
purchase  either  sheep  at  83.50  a  head,  calves  at  810.50,  cows 
at  835,  oxen  at  870,  or  horses  at  8105  ? 

186.  A  and  B,  traveling  together,  started  with  such  sums 
of  money  that  i  of  A's  was  equal  to  J3  of  B's ;  each  spent 
81 '2,  when  I  of  A's  money  was  equal  to  I  of  B's.  How 
much  did  each  start  with  ? 

187.  The  point  in  the  earth's  orbit  farthest  from  the  sun  is 
96600000  miles ;  the  point  nearest,  93400000  miles ;  of  the 
moon  from  the  earth  the  farthest,  251760  miles;  the  near- 
est, 221290  miles.  What  are  the  greatest  and  least  possible 
distances  between  the  sun  and  the  moon  ? 

188.  From  a  cistern  containing  3465  gallons.  62.75  barrels, 
of  31.5  gallons  each,  were  drawn  off.  How  many  gallons 
remained  ? 

189.  A  has  8647,  which  lacks  833  of  being  4  times  what 
B  has  ;  C  is  worth  twice  as  much  as  A  and  B  together,  lack- 
ing 872.     How  much  money  have  B  and  C  respectively  ? 

190.  A  merchant  bought  a  number  of  bushels  of  corn  ; 
having  sold  6  bushels  more  than  i  of  it  to  V>'.  Smith,  and  8 
bushels  more  than  |  of  the  remainder  to  J.  Acker,  ho  had  20 
bushels  remaining.     How  many  bushels  did  he  buy  ? 

191.  The  number  of  stamped  envelopes  sold  in  one  year 


64  ARITHMETICAL    EXAMPLES. 

were  as  follows:  three-oent  envelopes,  22940100;  one-cent, 
2845000;  four-cent,  70000;  six  cent,  40450;  ten-cent,  131- 
750;  allowing  5  cents  as  the  cost  of  paper  and  manufacturing 
every  package  of  25  envelopes,  what  was  the  whole  number 
sold  and  their  value  ? 

192.  Reduce  f,  j%,  ^4,  -^^  ^"^  H  ^^  ^^^^^^  ^^^^^  common 
denominator. 

193.  A,  B  and  C,  who  can  respectively  travel  3,  4  and  5 
miles  an  hour,  propose  to  walk  from  Springfield  to  Hartford, 
the  distance  being  26  miles.  How  many  hours  after  A  starts 
must  B  and  C  each  set  out,  that  all  may  reach  Hartford  at  the 
same  time  ? 

194.  In  the  battle  of  Chickamauga,  the  number  killed  was 
485  more  than  ^  the  wounded  ;  the  missing  were  13  more 
than  3  times  the  number  killed  ;  the  total  loss  being  15861, 
how  many  were  killed,  wounded  and  missing? 

195.  A  farmer  exchanged  50  loads  of  wood,  each  containing 
I  of  a  cord,  at  $4.40  per  cord,  for  an  equal  number  of  bushels 
of  corn  worth  $.75  a  bushel,  and  of  oats  worth  $.57  a  bushel. 
How  many  bushels  of  each  did  he  receive  1 

196.  A  has  6.4  acres  in  one  lot,  and  8.75  in  another ;  B 
has  4.375  acres  less  than  3  times  as  much  as  A ;  C  has  7.2875 
acres  less  than  ^  as  much  as  A  and  B  together.  How  many 
acres  had  B  and  C  ? 

197.  The  entire  population  of  Connecticut  in  1860,  was 
460146,  and  the  products  of  industry  were  $83056353  ;  allow- 
ing I  of  the  entire  population  to  be  engaged  in  industrial  pur- 
suits, what  was  the  average  value  of  the  labor  of  each  during 
the  year  ? 

198.  How  many  bushels  of  corn  must  a  farmer  carry  to 
mill  that  he  may  bring  back  3|  bushels,  provided  the  miller 
takes  jig  for  toll  1 

199.  Reduce  UhlU  ^^  '^^^  lowest  terms. 

200.  John,  Henry  aud   Charles  have  respectively  65,  91 


ARITHMETICAL    EXAMPLES.  65 

and  117  cents,  with  which  they  agree  to  purchase  tops  at  the 
highest  price  that  will  allow  each  one  to  spend  all  his  money. 
How  many  tops  can  each  buy  ? 

201.  Bought  a  quantity  of  lumber  for  ^TSS-j^^,  and  of  wood 
for  ^M7j  ;  sold  the  lumber  for  '$649*,  and  the  wood  for 
C^589J.     How  much  did  I  gain  ? 

20'2.  Hudson  County,  New  Jersey,  appropriated  $3723.03 
fjr  the  education  of  17501  children  for  one  year.  How  much 
was  appropriated  for  each  child '? 

203.  Two  men,  84.675  miles  apart,  traveled  till  they  met 
each  other,  when  they  found  that  one  had  traveled  8.425  miles 
farther  than  the  other.     How  far  did  each  travel  ? 

204.  How  many  bushels  of  potatoes  at  $|  per  bushel,  will 
pay  for  6|  bushels  of  wheat  at  '$1.40  per  bushel  ? 

205.  The  N.  Y.  Central  R.  R.  Company  owned,  in  18G2, 
650  miles  in  length  of  railroad,  which  cost  for  construction 
and  equipment,  831524226.  The  New  York  and  Erie  R.  R. 
Company  owned  446  miles  in  length,  which  cost  -S35796902. 
How  much  was  the  average  cost  per  mile  of  the  one  more 
than  of  the  other  ? 

206.  The  discharging  pipe  of  a  cistern  has  ?  the  capacity 
of  the  receiving  pipe,  which  will  fill  the  cistern  in  9.8  hours ; 
the  re€eiving  j^pe  has  been  open  4'~  hours,  when  the  discharging 
pipe  is  opened.  In  how  many  hours  after  will  the  cistern  bo  full  ? 

207.  There  were  2187480  pieces  of  gold,  silver  and  copper 
coined  at  the  U.  S.  Mint  in  one  month,  valued  at  $168908; 
2170000  were  copper  coins,  and  there  were  12002  silver  coins, 
valued  at  $6606.  What  was  the  average  value  of  the  gold 
coins  ? 

208.  If  I  of  I  of  I  of  I  of  a  ship  be  worth  §  of  ]  |  of  ]  f  of 
Y\  of  her  cargo,  how  many  times  the  value  of  the  ship  is  her 
cargo  worth  1 

209.  I  exchanged  30  barrels  of  molasses,  each  containing 
34  gallons,  at  8.56  a  gallon,  for  17  chests  of  tea  of  24  pounds 
each.     How  much  did  the  tea  cost  me  per  pound  ? 


66  ARITHMETICAL    EXAMPLES. 

210.  A  coal  dealer  sold  5  tons  of  coal  for  $57.50,  which 
was  I  as  much  as  he  received  for  all  he  had  left  at  $7.66 --  per 
ton.     How  many  tons  did  he  sell  ? 

211.  A  farmer  sold,  in  one  year,  150  bushels  of  oats  at 
^>.45  per  bushel ;  250.25  bushels  of  corn  at  eto.875  per  bushel ; 
75.75  cords  of  wood  at  13.625  a  cord;  645 1  pounds  of  wool 
at  $.78  per  pound ;  23  head  of  cattle  at  an  average  price  of 
$50.75  per  head.     How  much  did  he  receive  for  the  whole  ? 

212.  The  number  of  railroad  accidents,  in  the  U.  States,  in 
1862,  was  I  of  the  number  of  persons  killed  by  the  accidents; 
and  the  injured,  which  w^ere  877,  were  30  more  than  2J  times 
the  number  of  accidents  and  killed  together.  What  was  the 
number  of  accidents,  and  hov\^  many  were  killed? 

213.  Six  boys  divided  some  chestnuts  among  themselves ; 
James  took  |  of  them  wanting  6 ;  Thomas  took  6  less  than 
-]  of  the  remainder ;  John  took  5  less  than  A  of  what  still  re- 
mained ;  Henry  took  2  less  than  J-  of  what  then  remained ; 
William  took  5  less  than  |  of  the  residue,  and  George  took 
the  remainder,  which  was  25.  How  many  chestnuts  were  di- 
vided ? 

214.  In  1858,  9061504  bushels  of  wheat  were  sent  out  of 
the  country;  in  1859,2849192  bushels;  in  .1860,4076704 
bushels;  and  in  1861,38313024  bushels.  How  many  more 
bushels  were  exported  in  1861,  than  during  the  three  previous 
years  ? 

215.  What  number  is  that  whose  sixth  part  exceeds  its 
eighth  part  by  20  less  than  its  ninth  part  ? 

216.  A  speculator  sold  a  quantity  of  grain  for  $96,  and 
gained  ^  of  what  it  cost  him.  What  part  of  the  cost  would 
his  gain  have  been  had  he  sold  it  for  $100? 

217.  A,  B  and  C  can  perform  a  certain  piece  of  work  in 
26}^  days;  A,  B  and  D  in  29{A  days;  A,  C  and  D  in  33f 
days,  and  B,  C  and  D  in  ^42  days.  How  long  would  it  take 
each  to  do  it  alone  ? 


ARITHMETICAL    EXAMPLES.  C7 

218.  If  a  mason,  in  constructing  a  sewer,  650.25  feet  in 
length,  begin  with  a  diameter  of  32  inches,  and  increase  .1  of 
an  inch  in  every  foot  in  length.  How  many  times  the  diam- 
eter of  the  beginning  will  the  end  be  1 

219.  The  sales  of  sperm  oil  for  export  and  home  use,  at 
New  Bedford,  for  the  week  ending  Jan.  23,  18G4,  were  3488 
barrels,  of  31.5  gallons  each,  at  $1.65  per  gallon;  5.6  times 
the  quantity  for  home  use,  was  equal  to  1  ^  times  the  quanti- 
ty for  export.     What  was  the  value  of  the  exported  oil  ? 

220.  If  3/j  tons  of  coal  will  last  a^  long  as  4}-^-  cords  of 
wood,  how  many  tons  of  coal  will  last  as  long  as  13 /j  cords 
of  wood  ? 

221.  A  merchant  expended  $384  for  an  equal  number  of 
yards  of  six  different  kinds  of  broadcloth,  costing  respectively 
$2.00,  $3.00,  $3.50,  $4.00,  $4.50,  $7.00  per  yard.  How 
many  yards  of  each  kind  did  he  buy  1 

222.  How  many  rails,  of  the  longest  possible  equal  lengthy 
will  inclose  a  rectangular  field  9893  feet  long  by  804?  feet 
wide,  with  a  straight  fence  six  rails  high  1 

223.  In  1863  the  school  houses  built  of  brick  in  the  State 
of  New  York  were  -j\  the  whole  number +  16;  the  framed 
school  houses  were  10  more  than  10  times  the  brick;  the 
stone,  3  less  than  -^^  the  brick,  and  the  log  school  houses  ^vere 
33  less  than  |  the  brick.     Required  the  number  of  each  kind. 

224.  What  number  is  that  wdiose  J  part  being  subtracted 
from  its  ^,  the  remainder  will  be  4  less  than  i  the  number  ? 

225.  A  man  dying,  left  to  his  oldest  son  -|  of  the  estate,  in- 
creased by  j^(j  his  daughter's  share  ;  to  his  youngest  son  *  of 
the  estate  plus  ^  of  his  daughter's  share ;  and  to  his  daughter 
the  remainder,  v*'hich  was  $700  less  than  the  younger  son's 
share.     What  was  the  value  of  the  estate  1 

226.  A  grocer  has  forgotten  the  weight  and  first  cost  of  a 
box  of  cofiee ;  he  only  recollects  that  if  he  had  sold  it  at  28 
cents  a  pound  he  would  have  gained  $2.00,  but  if  he  had  sold 


68  AlilTHrvIETICAL    EXAMPLES. 

it  at  21  cents  a  pound  he  would  have  lost   $5.00.     Required 
the  number  of  pounds  in  the  box  and  the  first  cost  per  pound. 

3    Qf  o  4    of  _7_ 

227.  The  sum  of  ^-~  and  ,''  ,.-'-;-  is  equal  to  how  many 

.5  -g  ot  2.2o 

times  their  difference'? 

228.  During  the  year  18G1,  of  the  letters  exchanged  be- 
tween the  United  States  and  Great  Britain,  1707439  were  re- 
ceived, 1591644  were  sent;  between  the  United  States  and 
France,  C79184  were  received,  680577  sent.  How  many 
letters  did  the  exchange^  with  Great  Britain  exceed  that  with 
France  1 

229.  The  rate  of  postage  between  the  United  States  and 
Great  Britain  was  $.24  for  each  ^  ounce ;  between  the  United 
States  and  France,  $.30  ;  allowing  the  letters  to  weigh  A  ounce 
each,  how  much  greater  were  the  receipts  for  postage,  between 
the  United  States  and  Great  Britain  than  between  the  United 
States  and  Fr:nice  1 

230.  A  and  B  can  do  a  piece  of  work  in  Gj  days ;  B  and  C 
in  12  days;  and  A  and  C  in  10  days.  In  hov/  many  days 
could  all  working  together  do  it  1 

231 .  A  trader  bought  corn  at  $.63  per  bushel,  and  sold  it 
for  $.56.  How  much  did  he  lose  on  every  dollar  he  paid 
out? 

232.  A  boat  which  could  move  14  miles  an  hour  in  still 
water,  was  accelerated  2^  miles  per  hour  in  going  down 
stream,  and  retarded  the  same  in  coming  up  ;  it  was  10  hours 
longer  in  coming  up  a  certain  distance  than  in  going  down  the 
same.     What  was  the  distance  ] 

233.  The  difference  between  two  numbers  is  8,  and  j'j  of 
the  larger  is  equal  to  ]  of  the  smaller.  What  are  the  numbers'? 

234.  J.  Burke  engaged  to  work  a  year  for  $180  and  a  suit 
of  clothes;  at  the  end  of  8  months  he  was  disabled,  and  re- 
ceived for  his  wages  the  suit  of  clothes  and  $110.  What  was 
the  cost  of  the  suit  of  clothes  1 


ARITHMETICAL    EXAMPLES.  69 

235.  How  long  will  it  take  a  man  to  walk  486  miles,  if  he 
walk  3^  miles  an  hour,  and  7i  hours  each  day  ? 

236.  The  population  of  the  United  States  in  1840,  was 
17069453;  in  1850,23191876;  in  1860,  31445080.  How 
much  more  was  the  increase  for  every  hundred,  from  1840 
to  1850,  than  from  1850  to  1860  ? 

237.  A  grocer  exchanged  112.5  lb.  of  coffee,  for  tea  at  $.875 
per  lb.,  the  price  of  3f  lb.  of  coffee  being  equal  to  that  of  2 
lb.  of  tea.  How  many  pounds  of  tea  did  he  receive,  and  what 
•was  the  price  of  his  coffee  per  pound  1 

238.  A  tree,  by  falling,  was  broken  into  3  pieces;  the  top 
part  was  15  feet  long ;  the  bottom,  as  long  as  the  top  and  -\ 
the  middle  piece,  and  the  middle  part  as  long  as  the  top  and 
bottom.     What  was  the  height  of  the  tree  1 

239.  How  far  may  a  person  ride  in  a  coach,  which  goes  10 
miles  an  hour,  so  that  he  may  be  gone  3  hours,  provided  he 
walk  back  at  the  rate  of  4  miles  an  houi  1 

240.  If  it  is  worth  |.80  to  saw  a  cord  of  wood  consisting  of 
sticks  4  feet  long,  into  pieces  1  i  feet  in  length,  how  much  is  it 
worth  to  saw  a  cord  consisting  of  sticks  8  feet  long,  into 
pieces  of  the  same  length  ? 

241.  What  number  is  that  which  being  increased  by  |  of 
_T^  of  /i  of  itself,  will  amount  to  247|  1 

242.  The  forward  wheels  of  a  carriage  are  10.5  feet  in  cir- 
cumference, and  the  hind  wheels  15  feet.  The  places  where 
the  tires  are  welded  together  in  each  wheel  were  up  together 
when  the  carriage  started,  and  when  it  stopped  the  same  places 
were  up  together  for  the  352nd  time.  Required  the  number 
of  miles  the  carriage  had  traveled,  allowing  5280  feet  to  a 
mile? 

243.  A  and  B  set  out  from  the  same  place,  and  in  the  same 
direction;  A  traveled  16  miles  a  day,  and  after  traveling  7} 
days  turned  and  went  back  as  far  as  B  had  traveled  in  7^} 
days ;  he  then  turned  again,  and  pursuing  his  journey,  over- 


70  AraTiiMJi:TiCAL  EXA3irLii:3. 

took  B  25  days  after  they  first  set  out.     How  far  did  B  travel 
each  day  '? 

244.  If  10  oxen,  or  14  cows,  eat  4/^  tons  of  hay  in  58  days, 
in  what  time  will  4  oxen  and  6  cows  eat  the  same  quantity  of 
hay? 

245.  Ill  the  State  of  New  York  72104  children  attended 
school  more  than  10  months  of  a  certain  year;  65161,  more 
than  8  months;  115450,  more  than  6  months;  176221,  more 
than  4  months ;  240328,  more  than  2  months,  and  217551,  less 
than  2  month.^.  How  many  children  of  school  age  did  not 
attend  school  at  all,  the  whole  number  being  1357047  ? 

246.  Six  men  can  do  a  piece  of  work  in  7j  days.  How 
soon  after  beginning  must  they  be  joined  by  2  more,  so  as  to 
complete  it  in  5|  days  ? 

247.  Bought  a  western  fiirm  for  $11180,  and  after  expend- 
ing f>871  in  improvements,  I  sold  one  half  of  it  for  $7740,  at 
$18  per  acre.  How  many  acres  of  land  did  I  purchase,  and 
at  what  price  ? 

248.  How  many  times  is  the  greatest  common  divisor  of 
4J,  6t1,  7|  and.7,'\,  contained  in  the  least  common  multiple 
of  the  same  numbers  ? 

249.  When  one  dollar  of  gold  is  worth  159^  cents,  liow 
many  wiiole  dollars  in  gold  ought  a  broker  to  pay  for  a  ten- 
dollar  U.  S.  note,  and  how  much  fractional  currency  ? 

250.  A  hound  ran  200  rods  before  he  caught  a  fox ;  -|  the 
distance  the  fox  ran  before  being  caught  was  equal  to  the  dis- 
tance he  was  in  advance  when  they  started.  How  far  in  ad- 
vance was  the  fox,  and  how  far  did  he  run  ? 

251.  The  State  Superintendent  of  Schools  in  Pennsylvania 
reported,  in  1862,  that  98  more  than  I  the  whole  number  of 
school  houses  in  the  State  were  wholly  unfit  for  use  ;  that  25 
more  than  twice  this  number  were  improvable,  so  as  to  an- 
swer for  school  purposes ;  and  the  remainder,  4133,  were 
suitable  in  all  respects.  How  many  school  houses  in  the 
State  ? 


ARITHMETICAL    EXAMPLES.  71 

252.  Twelve  men  can  do  a  piece  of  work  in  8|  days ;  how 
many  days  may  S  remain  away,  and  yet  finish  the  work  in 
the  same  time,  by  bringing  7  more  with  them  1 

253.  In  1860,  Virginia  produced  12396775  lbs.  of  tobacco, 
at  an  average  value  of  'li.lO  per  lb.  How  many  school 
houses,  at  a  cost  of  81150,  and  how  many  churches,  at  a  cost 
of  '^8550,  of  each  an  equal  number,  could  be  built  with  the 
proceeds  of  the  tobacco  crop  1 

254.  A  boy  spent  one-third  of  his  money  for  apples,  and 
20  cents  for  nuts  ;  he  then  gave  10  cents  more  than  one-fourth 
of  the  remainder  for  oranges,  when  he  found  he  had  but  50 
cents  left.     How  many  cents  had  he  at  fa^st  ? 

255.  Divide  $14500  between  A  and  B,  so  that  A  shall 
have  I  as  much  as  B,  increased  by  82500. 

256.  In  a  lot  of  silver  change,  worth  813.50,  ?  of  the  value 
is  in  50-cent  pieces,  4  of  the  remainder  in  25-cent  pieces,  and 
the  rest  is  made  up  of  10-cent,  5-cent  and  3-cent  pieces,  of 
each  an  equal  number.  How  many  j)ieces  of  each  coin  are 
there  I 

257.  ]f  a  cubic  foot  of  granite  weigh  168.48  pounds,  what 
will  be  the  weight  of  a  block  of  granite  10.75  feet  long,  4.5 
feet  wide,  and  3.8  feet  thick  1 

258.  The  United  States  has  an  area  of  2319811  square 
miles,  and  a  population  of  31445080.  Europe  has  an  area 
of  3757209  square  miles,  and  a  population  of  268851381. 
What  is  the  difference  in  area  and  population  ? 

251).  Divide  the  sum  of   .^  of.  4  of  28  -r^  and  S^p   by  the. 
^        ^  4|  lOo     -^ 

34i98i   2.1  128 

continued  product  of  -——■,  — ^tt'  -^  ^^^^  r~i~'' 
27     b<§    I  81 y\ 

260.  John  and  James  started  together  and  ran  a  race ; 
when  James  had  run  80  rods,  y^^  the  distance  John  had  run 
was  equal  to  the  distance  he  was  ahead  of  James.  How 
much  did  John  gain  on  James  in  running  80  rods  1 


72  ARITHMETICAL    EXAMPLES. 

201.  A  £;chool  house  which  cost  $980  is  to  be  paid  for  by 
four  men,  A,  B,  C  and  D.  It  is  agreed  that  each  shall  pay 
according  to  his  nearness  to  the  school  house.  A  is  twice  as 
near  as  B,  and  B  is  |  as  near  as  C,  who  is  |  as  near  as  D. 
IIo^y  inuch  ought  each  to  pay  1 

8G2.  If  14  men  can  perform  a  job  in  27  days,  in  how  many 
days  can  they  perform  the  same  labor  with  the  assistance  of 
7  more  men  ? 

263.  The  value  of  books  printed  in  New  York,  in  18G0, 
was  $6920102;  of  job  work,  ^2574529;  of  newspapers, 
Si 3422254.  The  aggregate  value  of  printing  in  the  United 
States  for  the  same  period  was  139678043.  How  much 
more  than  one-half  the  value  of  the  whole  printing  was  done 
in  New  York  ? 

264.  A  can  travel  around  a  certain  island  in  2^^  days,  B 
in  31  days,  and  Cm  3]  days.  U  they  all  set  out  from  the 
same  point,  and  travel  the  same  way,  in  how  many  days  will 
they  all  meet  at  the  point  from  which  they  started  ? 

265.  The  total  cost  of  maintaining  schools  in  the  State  of 
New  York,  in  1863,  was  $3859159.21.  The  rural  districts 
raised  by  taxation  $503181.28,  by  rate  bills,  $363741.05;  the 
cities  raised  by  taxation  $1595728.80;  the  remaining  cost  was 
paid  by  the  State  School  Fund  ?  What  amount  of  money 
was  received  from  the  State? 

266.  A  man  laid  out  |  of  his  fortune  in  speculation,  and 
put  out  on  interest  the  remaining  $6800 ;  at  the  end  of  the 
year  he  had  gained  f?^  as  much  by  speculation  as  he  laid  out, 
and  his  interest  was  ^  of  the  principal.  What  was  his  for- 
tune, and  how  much  did  he  gain  during  the  year  ? 

267.  A  man  bought  2400  bushels  of  corn,  at  $.90  a  bushel, 
but  in  measuring  it  he  found  that  he  had  more  bushels  than 
he  paid  for,  and  that  he  had  gained  2.25  bushels  for  every 
hundred.  He  sold  the  same  without  delay  at  $1.05  a  bushel. 
How  much  did  he  make  by  the  transaction  ? 


ARITHMETICAL   EXAMPLES.  73 

2GS.  A  man  has  2  horses  and  a  saddle ;  if  the  saddle  be 
placed  upon  the  first  horse,  valued  at  $60,  it  will  make  him 
1|  times  the  value  of  the  second  horse,  but  if  it  be  put  on  the 
second  horse,  it  will  make  his  value  twice  that  of  the  first  horse. 
Eequired  the  value  of  the  saddle  and  the  second  horse. 

269.  In  ISGl,  there  were  2819S11  square  miles,  of  640 
acres  each,  in  the  United  States;  and  there  were  1155510 
farms,  of  215  acres  each,  under  cultivation.  How  many 
acres  were  still  uncultivated  1 

270.  The  above  farms  were  each  valued  at  an  average  of 
$5756,  and  upon  each  farm  there  was  an  average  of  1213  in 
machinery  and  implements.  What  was  the  aggregate  value 
of  the  firms  and  implements  1 

271.  Bought  a  bale  of  cloth  for  ^96.75,  and  disposed  of  it 
for  §  the  cost,  by  which  I  lost  $1.00  on  a  yard.  IIow  many 
yards  were  there  in  the  bale  ? 

272.  There  is  a  cask  containing  brandy  and  water ;  |  of 
the  whole  +  4  gallons,  is  brandy,  and  J  of  the  whole  +  2 
gallons  is  water.     IIow  many  gallons  of  each  ? 

273.  A  had  |  of  |  of  3 J  times  $31443,  and  paid  |  of  l  of 
■{'q  of  it  for  a  farm.     How  much  money  had  he  remaining? 

274.  Bought  7.5  lb.  of  sugar  for  $.37.1.  For  how  much 
must  I  sell  5.25  lb.,  to  gain  the  cost  of  .25  of  a  lb.  1 

275.  The  New  England  States  had  sent  into  the  army,  Jan. 
1,1863,  183732  men;  the  Middle  States,  453386  ;  the  West- 
ern States,  103887  more  than  the  Middle  States ;  the  Border 
States  101877  less  than  the  New  England  States.  Of  the 
whole  number,  91561  were  three-months  men,  67335  nine- 
months  men,  and  48571  were  enlisted  for  irregular  periods; 
the  remainder  enlijtcd  for  three  years.  IIov,r  many  of  this 
class  were  there  ] 

276.  A  man  divided  $670  among  his  3  sons,  so  that  ]  the 
share  of  the  first  was  equal  to  J  the  share  of  the  second,  and 
to  I  the  share  of  the  third.     Required  the  several  shares. 


74  ARITHMETICAL    EXAMPLES. 

277.  Bought  24  tons  of  hay,  at  116.50  per  ton,  for  |  of 
which  1  paid  sheep,  at  $S'~  each,  and  for  the  remainder  I  paid 
butter,  at  '1>.19i  per  pound.  How  many  sheep  and  how  many 
pounds  of  butter  did  it  require  to  pay  the  debt '? 

278.  Bought  17  chests  of  tea,  each  containing  59  pounds, 
at  $.67  a  pound,  and  gave  in  exchange  118  bags  of  wheat, 
each  containing  3.4  bushels.  What  was  the  value  of  the 
wheat  per  bushel  ? 

379.  The  value  of  the  flour  and  meal  produced  in  the 
United  States,  in  1860,  was  $224000000;  of  cotton  goods, 
three  million  of  dollars  more  than  one-half  the  value  of  the 
corn  and  meal ;  of  boots  and  shoes,  J  |  the  value  of  cotton 
goods ;  of  clothing,  |  the  value  of  the  boots  and  shoes  ;  of 
printing,  |  the  value  of  the  clothing.  IIow  much  did  the 
sum  of  the  values  of  the  printing,  and  boots,  and  shoes,  exceed 
in  value  the  cotton  goods'? 

280.  The  circumference  of  a  circle  is  always  3.141592 
times  the  diameter.  Ilovr  many  revolutions  will  a  carriage 
wheel,  which  is  3 A  feet  in  diameter,  make  in  going  a  distance 
of  5.73  miles? 

281.  A  flither  divided  a  piece  of  land  among  his  three 
sons.  To  the  fu'st  he  gave  16.25  acres;  to  the  second,  -j^^  of 
the  whole;  and  to  the  third,  as  much  as  to  the  other  two. 
IIow  many  acres  liad  the  third  ] 

282.  The  British  army  in  India,  in  1863,  consisted  of  7062 
cavalry;  twice  as  many  artillery,  lacking  124;  and  4  times 
as  many  infantry  as  artillery,  lacking  1163.  The  cavalry  in 
the  home  army  were  66  more  than  the  artillery  in  the  India 
army,  and  the  infanti'y  2968  more  than  9  times  the  home  cav- 
alry. What  was  the  aggregate  strength  of  the  home  and 
of  the  India  army  1 

283.  A  market  woman  bought  a  number  of  peaches  at  the 
rate  of  2  for  1  cent,  and  as  many  more  at  the  rate  of  3  for  2 
cents,  and  sold  them  all  at  the  rate  of  5  for  3  cents,  gaining 
4  cents.     IIow  many  peaches  did  she  buy '? 


ARITHMETICAL    EXAMPLES.  75 

284.  A  tree  164  feet  high,  in  falling  was  broken  into  two 
pieces,  of  such  lengths  that  |  of  one  piece  equaled  ^  of  the 
other.     Required  the  length  of  the  pieces. 

285.  In  Wisconsin,  the  number  of  stone  and  brick  school 
houses,  in  18(31,  was  376;  of  framed,  2478;  of  log,  1357; 
the  average  cost  of  these  buildings  was  1309.50.  What  was 
the  cost  of  all  the  school  houses  ? 

286.  If  3J  yds.  of  cloth.  If  yds.  wide,  cost  $3.46~,  what 
will  be  the  cost  of  42|  yds.,  IJ  yds.  wide*? 

287.  A  piece  of  land  was  divided  into  two  parts,  so  that  -^ 
the  first  was  equal  to  -]  the  second.  The  difference  between 
the  two  parts  was  10.7534  acres.  What  was  the  whole 
amount,  and  what  were  the  parts  1 

288.  What  is  the  value  of  the  following  expression :  |  of 
71       J^  8        6  1         -3_      oo 

5  ^3.7  •    ^""^  ^'^     2.15^  i  ^      4j^3^3i) 

289.  A  garden  whose  breadth  is  9  rods,  and  whose  length 
is  1|  its  breadth,  has  a  wall  3|  feet  thick  around  it.  What 
was  the  cost  of  digging  a  trench  2|  feet  deep,  in  which  to  lay 
this  wall,  at  1 5  cents  per  cubic  foot  1 

290.  There  were  38068  children  attending  school  in  614 
districts  in  California,  in  1861.  The  whole  cost  of  schools  for 
the  year  was  8470115.24.  What  was  the  average  number 
attending  in  each  district,  and  what  the  average  expense  per 
scholar  ? 

291.  Three  horses  start  from  the  same  point,  and  at  the 
same  time,  upon  a  race-course  300  rods  in  circuit ;  the  first 
horse  passing  over  h  the  circuit,  the  second  |,  the  third  J,  in 
a  minute.  In  how  many  minutes  will  they  all  be  together 
again,  and  how  far  will  each  have  traveled  ? 

292.  Bought  4  bushels  of  wheat,  and  3^  times  as  many, 
bushels  of  corn ;  for  the  former  I  paid  |  as  many  dollars  per- 
bushel  as  there  were  bushels  of  the  latter,  and  for  the  latter 
I  as  much  per  bushel  as  for  the  former.  Required  the  price 
of  each  per  bushel,  and  the  vrhole  cost  1 


CPIAPTEE  lY. 

1.  The  source  of  the  river  Volga  is  550  feet  above  the  level 
of  the  sea ;  after  a  course  of  2000  miles  it  empties  into  the 
Caspian  sea,  which  is  83  feet  below  the  surface  of  the  ocea'.i. 
How  much  is  the  average  full,  per  mile,  of  the  river  1        < 

2.  A  physician  bought  by  Avoirdupois  Weight,  15  ib. 
opium  at  4  cents  a  dram,  and  sold  the  same  by  Apothecai'ies' 
Weight,  in  doses  of  10  grains  each,  for  25  cents  per  dose. 
How  much  did  he  gain '? 

3.  The  amount  of  money  in  the  Sub-Treasury  in  New 
York,  Jan.  1st,  18G4,was  $12898926.81);  the  amount  received 
in  January,  on  account  of  Customs,  was  $6179005.51  ;  of 
Loans,  $37463895.94 ;  of  Internal  Revenue,  $2275400.67 ;  of 
Transfers,  $300000.00;  of  Patent  Fees,  $6613.65;  of  Miscel- 
laneous, $4164352.27;  of  Post  Office  Department,  $108982.- 
51 ;  and  the  amount  paid  out  in  Treasury  Drafts  was  $48343- 
806.66 ;  in  Post  OfKce  Drafts,  $82663.06.  How  much  re- 
mained in  the  Treasury,  Feb.  Ist,  13G4? 

4.  How  much  land  in  New  York  at  $2.25  per  square  foot 
will  $200000  buy  ? 

5.  The  population  of  London,  in  1860,  was  2S00000  ;  the 
number  of  deaths  during  the  year  was  63644  ;  the  population 
of  New  York,  at  the  same  time,  was  805600,  and  the  number 
of  deaths,  18126.  How  many  more  deaths  per  million  in 
London  than  in  New  York  ? 

6.  A  man  and  his  son  w\alk  from  Hartford  to  Now  Haven, 
a  distance  of  36  miles ;  allowing  that  the  man  pns';es  over  a 
distance  of  2  ft.  9  in.  at  each  step,  and  the  boy  a  distance  of 
1  fr.  10  in.,  how  many  more  steps  does  the  boy  take  than  the 
man. 


ARITHMETICAL    EXAMPLES.  77 

7.  A  school  room,  which  is  36  fr.  long,  30  ft.  wide,  and  12 
ft.  high,  is  occupied  by  80  pupils,  each  breathing  10  cu.  ft.  of 
air  in  one  minute.  In  how  long  a  time  will  they  breathe  as 
much  air  as  the  room  contains  ? 

8.  What  is  the  sum  of  /''^f^^^,,,  and  i^^  ? 

is^Hxii)  1.0  X. 625 

•  9.  A  man  having  a  hogshead  of  molasses,  sold  Ys  of  it  to 
A,  I  of  the  remainder  to  B,  and  ]  of  the  residue  to  C.  How 
many  gallons  remained  ? 

9_T. 

10.  What  is  the  value  of  ~4|  of  a  dollar  ?  - 

11.  Bought  78  A.  3  R.  15  P.  7  sq.  yd.  5  sq.  ft.  9  sq.  in.  of 
land  at  880  per  acre ;  I  sold  |  of  it  to  A  at  $120  per  acre ;  | 
of  the  remainder  to  B  at  ^1.00  per  sq.  rd.,  and  the  residue 
to  C  at  8.005  per  sq.  ft.     W^hat  was  my  whole  gain  ? 

12.  A  fruit  dealer  bought  4  barrels  of  cranberries,  each 
containing  2A  bushels  at  88.00  per  barrel ;  he  retailed  the 
same  at  12^  cents  per  quart,  wme  measure.  How  much  -was 
his  profit  ? 

13.  ^  of  the  muskets  captured  at  the  battle  of  Gettysburg 
by  the  U.  S.  army  were  loaded ;  i  of  these  contained  one 
charge  each;  A,  two  charges  each;  |,  from  three  to  ten  each; 
g-^^pg,  from  ten  to  fifteen  each,  and  the  remainder,  which  was 
40,  from  fifteen  to  twenty-three  each.  How  many  muskets 
were  captured  ? 

14.  The  distance  from  Albany  to  Buffalo  is  298  miles  ;  an 
express  train  from  Albany,  and  a  mail  train  from  Buffalo, 
start  at  the  same  time ;  the  express  runs  at  the  rate  of  24 
miles  per  hour,  and  the  mail  train,  20  miles ;  for  each  hour 
of  running  time  the  express  stops  6  minutes,  and  the  mail 
train,  12  minutes.  How  many  hours  before  ihcy  meet,  and 
how  far  from  each  city  ? 

15.  The  total  yield  of  nine  copper  mines  in  1862,  was 
3942  T.  12  cwt.  1  qr.  1  lb. ;  in  1863,  the  same  mines  yielded 


78  ARITHMETICAL    EXAMPLES. 

4101  T.  8  cwt.  3  qr.  3  lb.;  if  copper  was  worth  20  cents  per 
pound,  of  how  much  greater  value  was  the  amount  produced 
in  1863,  than  in  1862? 

16.  In  the  Maine  House  of  Bepresentatives  in  1863,  the 
number  of  lawyers  was  5  more  than  the  editors ;  the  clergy- 
men, 2  more  than  the  lawyers ;  the  merchants  17  more  than 
the  clergymen,  and  17  less  than  the  farmers,  who  were  1  mo»e 
than  ^  the  whole  number.  What  was  the  number  of  each 
class  ? 

17.  A  man  took  5  loads  of  turnips  to  market,  each  load 
containing  16  bags,  and  each  bag  3  bushels ;  he  sold  them  for 
20  cents  a  bushel,  and  received  in  payment  4  boxes  of  sugar, 
each  box  containing  8  papers,  and  each  paper  15  lbs.  What 
was  the  price  of  the  sugar  per  pound  ? 

18.  Sold  72  yds.  carpeting  at  $1.37.^  a  yd.,  and  gained 
thereby  $18.     How  much  did  it  cost  me  per  yard  ? 

19.  A  merchant  carried  on  business  three  years ;  the  first 
year  he  gained  a  sum  equal  to  j\  of  his  original  capital ;  the 
second  year  he  lost  |  of  what  he  had  at  the  end  of  the  first 
year ;  the  third  year  he  gained  y^^  of  what  he  had  at  the  end 
of  the  second  year;  he  then  had  $14625.  How  much  had  he 
gained  in  the  three  years  1 

20.  A  flirmer  exchanged  26  bu.  1  pk.  6  qts.  of  oats  for  22 
bu.  4  qts.  of  salt.  What  quantity  of  oats  must  be  brought 
to  the  same  market  by  a  farmer  who  wishes  to  get  73  bu.  3 
pks.  of  salt? 

21.  Divide  637  A.  3  R.  8  P.  11  sq.  yds.  4  sq.  ft.  16  sq.  in. 
by  16. 

22.  A  pedestrian,  in  training  for  a  foot  race,  traveled  75  mi. 
3  fur.  37  rd.  5  yd.  2  ft.  10  in.  the  first  week  ;  the  second  week, 
89  mi.  3  fur.  9  rd.  2  yd.  1  ft.  10  in. ;  the  third  week,  127  mi. 
6  fur.  9  rd.  1  yd.  3  ft.  10  in.  How  far  did  he  travel  in  the 
three  weeks  ? 

23.  If  a  person  count  90  a  minute  for  10  hours  each  day, 
how  long  will  it  take  him  to  count  a  million'? 


ARITHMETICAL   EXAMPLES.  79 

2-1.  Bought  a  lot  25  rods  long  and  20  rods  wide  for  $10- 
000,  and  sold  the  same  at  25  cents  per  square  foot.  How 
much  was  my  gahi  ? 

25.  Simplify  the  following  fractions : 

1     :M 

I      7j         7        207 

I  ^  1_     .003]     500'  . 
.Og      "25 

26.  A  cellar  is  26  feet  long,  18  feet  wide,  and  7  feet  deep. 
How  much  earth  must  be  removed  to  make  it  28  feet  long,  21 
feet  wide,  and  8  feet  deep  1 

27.  How  many  square  yards  in  the  walls  of  a  room  40  feet 
long,  3H  feet  wide  and  12  feet  high  ? 

28.  A  person,  being  asked  the  time  of  day,  replied  :  "  llj 
times  the  time  past  noon  is  equal  to  4]  times  the  time  till 
midnight."     What  was  the  time  '? 

29.  I  purchased  some  pens  at  two  for  a  cent,  and  1.5  times 
as  many  at  3  for  2  cents ;  I  sold  them  all  at  the  rate  of  one- 
half  a  cent  each,  and  lost  15  cents  by  the  transaction.  How 
many  of  each  kind  did  I  buy  ? 

30.  The  market  value  being  the  same  in  both  States,  a 
farmer  from  New  Jersey  exchanged  50  bushels  of  buckwheat, 
worth  |l|  a  bushel,  with  a  farmer  in  New  York,  for  oats, 
worth  ^.40  abushel,  which  he  sold  in  his  own  State  for  cash. 
The  exchange  being  made  by  weight,  in  whose  favor  was  the 
diiference,  and  how  much  in  cash  value  1 

31.  What  will  4?  bales  of  cloth  cost,  each  bale  containing 
43.75  yards,  at  $.75  a  yard  ? 

32.  A  man  worked  3  months,  25  days  each  month,  10 
hours  each  day,  for  $.03  an  hour,  and  received  in  payment  2 
loads  of  grain,  each  containing  15  bags  of  2h  bushels  each. 
What  was  the  price  of  the  grain  per  bushel  1 

33.  I  bought  397  barrels  of  flour,  at  $9,025  per  barrel ; 
290  bushels  of  corn,  at  |.93  per  bushel  j  48  barrels  of  beef. 


80  ARITHMETICAL    EXAMPLES. 

at  $.09  per  lb. ;  170  barrels  of  pork,  at  $M-\  per  lb. ;  and 
225  cords  of  wood,  at  ^.87^  per  cord  foot.  What  was  the 
diiTerence  in  value  between  the  sum  of  the  cost  of  the  flour 
and  the  corn,  and  the  sum  of  the  cost  of  the  other  articles  ? 

34.  How  many  tons  of  hay,  at  ^.75  per  cwt.,  must  be  given 
for  35  cords  of  wood,  at  $.60  per  cord  foot  ? 

05.  It  is  estimated  that  the  Falls  of  Niagara  have  receded 
50  yards  within  the  last  40  years.  How  long  at  this  rate  has 
it  taken  them  to  recede  from  Lewiston,  6  miles  below  their 
present  site  ? 

36.  The  amount  expended  in  work  upon  the  canals  ni  New 
York,  in  1863,  was  as  follows,  viz. :  Champlain  Canal,  $48- 
195.95;  Black  River,  ^3261.77;  Erie,  $151435.42 ;  Oswego, 
$15456.02;  Cayuga,  $19755.58;  Baldwinsville,  $25015.88; 
Chemung,  $15083.20;  Crooked  Lake,  $28895.62  ;  Chenango, 
$16935.21 ;  Genesee  Valley,  $88292.75 ;  for  work  done  by 
Canal  Superintendents,  $107626.51.  What  was  the  whole 
amount  1 

37.  The  total  cost  of  engineering  upon  the  above  men- 
tioned canals  was  $31223.11.  How  much  was  expended  in 
work  for  $1  in  engineering? 

38.  What  part  of  5  da.  23  h.  58  min.  is  4  da.  6  h.  50 
min.  ? 

39.  Bought  7000  bushels  of  corn  in  Chicago  at  $.80  a 
bushel;  I  shipped  the  same  to  Buffalo,  and  sold  it  at  an  ad- 
vance of  20  cents  per  bushel ;  the  expenses  for  freight  and 
handling  the  grain  were  $500  :  the  corn  being  bought  and  sold 
by  weight,  how  much  did  I  gain  or  lose  ? 

40.  Nineteen  lots  of  equal  size  contain  159  A.  2  R.  17  sq. 
rd.  25  sq.  yd.  8  sq.  ft.  130  sq.  in.  What  is  the  value  of  one 
lot,  the  land  being  worth  half  a  dollar  per  square  foot  ? 

41.  A  spent  ^  his  money  and  gave  away  $20;  he  then 
spent  i  the  remainder  and  gave  away  $10  less  than  -}  of  what 
then  remained,  and  found  he  had  $48  left.  How  much  had 
he  at  first  ? 


ARITHMETICAL    EXAMPLES.  81 

42.  The  amount  of  cheese  made  in  the  State  of  New  York, 
in  1860,  was  48548-288  lbs.  Suppose  each  cheese  to  weigh 
64  lbs.,  and  to  be  20  in.  in  diameter,  how  many  miles  in 
length  would  they  extend  if  placed  in  a  line  ? 

43.  Thirty-two  men  agree  to  build  14  mi.  5  far.  34  rd.  6  ft. 
of  road  ;  when  the  work  is  i  done  they  employ  8  n^ore  men. 
What  distance  does  each  man  construct  ? 

44.  The  total  vote  for  Governor  in  Kentucky,  in  1863,  was 
85695,  of  which  Bramlette,  the  succest>ful  candidate,  received 
50917  more  than  Wickliife,  his  rival?  How  many  votes  did 
each  receive  ? 

45.  A  housebreaker,  having  been  brought  before  a  iudge, 
it  was  proved  that  he  had  stolen  property  to  the  value  of  £9 
12s.  9d,  3  far. ;  he  was  sentenced  to  pay  at  the  rate  of  £9  12s. 
9d.  3  far.  for  every  pound  stolen.     How  much  was  the  fine "? 

46.  A  and  B  started  together  by  railroad  from  Philadv.1- 
phia  for  Pittsburg,  the  distance  being  356  miles;  A  traveled 
by  express,  at  the  rate  of  SO  miles  per  hour;  B  by  mail 
train,  at  the  rate  of  25  miles  per  hour ;  C  left  Pittsburg  for 
Philadelphia,  at  the  same  time,  by  fast  line,  at  the  rate  of  32 
miles  per  hour.  How  far  from  Philadelphia  were  A  and  B 
respectively,  when  C  passed  them'? 

47.  What  is  the  value  of  .6923828125  cwt.  of  coffee  at 
38 1  cents  pound  ? 

48.  A  wood-dealer  delivered  a  quantity  of  wood  at  a  fac- 
tory ;  it  was  in  three  piles,  the  first  was  18  ft.  G  in.  long,  7  ft. 
6  in.  high,  and  4  ft.  wide ;  the  second  was  16  ft.  9  in.  long,  6 
ft.  9  in.  high,  and  4  ft.  6  in.  wide ;  the  third  was  20  ft.  3  in. 
long,  7  ft.  4  in.  high,  and  4  ft.  6  in.  wide.  How  many  cords 
were  delivered  ? 

49.  A  farmer  sold  19  bushels  of  rye  and  23  bushels  of  bar- 
ley for  §44.85;  he  received  for  the  rye  15  cents  more  per 
bushel  than  for  the  barley.  What  was  the  price  of  each  per 
bushel  ? 

50.  Sold  4  village  lots ;    the  first  contained   J  of  ?  of  an 


82  ARITHMETICAL   EXAMPLES. 

acre  ;    the  second  40^  rods ;    the  third  J  of  an  acre,  and  the 
fourth  ^  of  g  of  an  acre.     How  much  land  in  the  four  lots  ? 

51.  A  man  bought  a  horse  and  two  carriages;  for  the  first 
carriage  he  paid  $250  ;  if  this  sum  were  added  to  what  he 
paid  for  the  horse,  it  would  amount  to  §  of  the  sum  he  paid 
for  the  second  carriage ;  if  the  sum  he  paid  for  the  horse  were 
added  to  the  sum  paid  for  the  second  carriage,  it  would 
aniount  to  three  times  the  sum  paid  for  the  first  carriage. 
What  did  he  pay  for  each  ? 

52.  How  far  does  a  team  walk  in  plowing  an  acre,  allow- 
ing 10  inches  for  each  furrow? 

53.  The  aggregate  receipts  of  the  railroads  in  Pennsylvania 
for  1863  were  H0523571 ;  the  expenses  were  I20G02804. 
How  much  were  the  net  earnings  1 

54.  How  much  beef,  at  7d.  per  pound,  ought  I  to  receive 
for  27  lb.  12  oz.  of  butter  at  Is.  9d.  per  pound  ? 

55.  A  ship  at  the  equator  in  20°  30'  W.  longitude,  sailed 
due  West,  until  its  longitude  was  3G°  18'  W.  How  many 
statute  miles  did  the  ship  sail  1 

56.  There  were  three  candidates  for  the  office  of  Mayor  in 
the  city  of  New  York,  Dec.  1863,  and  there  were  71101  votes 
polled;  the  successful  candidate  received  6524  votes  more 
than  one  competitor,  and  9738  more  than  the  other.  How 
many  votes  did  each  receive  ? 

57.  If  a  town,  10  miles  square,  be  divided  equally  into  300 
farms,  v/hat  will  be  the  size  of  each  farm] 

58.  How  much  must  be  paid  for  a  pile  of  wood  12|  ft. 
long,  3|  ft.  wide,  and  3A  ft.  high,  at  1.64  per  cord  foot? 

59.  In  the  city  of  Springfield,  Mass.,  for  the  year  1803  the 
number  of  scholars  in  the  mixed  schools  was  272,  which  was 
l§  of  the  number  in  the  primary  schools;  f  |  of  the  number  in 
the  primary  schools  were  equal  to  the  number  in  the  inter- 
mediate schools,  which  was  2J  times  the  number  in  the  gram- 
mar schools ;    the  number  in  the  high  school  was  1  less   than 


ARITHMETICAL   EXAMPLES.  83 

-^^  the  number  in  the  grammar  schools ;  required  the  number 
in  each  grade  of  schools. 

60.  The  annual  expense  of  the  schools  in  the  above-men- 
tioned city  was  823302.50.  Now  if  the  expense  per  scholar 
was  the  same  in  the  mixed  schools  as  in  the  primary,  and  in 
the  intermediate  1|  times  as  much;  in  the  grammar  schools 
1|  times  as  m.uch  as  in  the  intermediate;  and  in  the  high 
school  2 J  times  as  much  as  in  the  grammar  school.  What 
was  the  expense  of  each  grade  of  school  for  the  yea^  ? 

Gl.  A  gentleman  travelling  west  from  Boston,  which  is 
71°  3'  W.  longitude,  finds,  on  his  arrival  at  St.  Louis,  that  his 
watch  is  1  h.  17  m.  24  sec.  faster  than  the  time  at  the  latter 
place ;  if  his  watch  has  kept  accurate  time,  what  is  the  longi- 
tude of  St.  Louis  1 

62.  What  will  be  the  cost  of  9  gal.  3  qt.  1  pt.  2  gi.  of  kero- 
sene oil  at  6s.  8d.  per  gal..  New  York  currency  ? 

63.  Express  in  acres  and  the  decimal  of  an  acre  the  area 
of  49  square  lots,  each  measuring  5  rd.  8  ft.  3  in.  on  a  side. 

64.  Tlie  number  of  cents  coined  at  the  U.  S.  mint  in  Phila- 
delphia during  the  month  of  January,  1804,  was  220800;  the 
silver  coinage  was  -J  the  value  of  the  cents,  and  also  |  the  value 
of  the  silver  deposits ;  the  deposits  of  silver  were  20  dollars- 
more  than  j*^  of  the  gold  coinage,  which  was  ^  ^^  the  gold 
deposits.     Required  the  sum  of  the  deposits  and  of  the  coinage. 

65.  Bought  48  bushels  corn  at  6s.  6d.  per  bushel.  New 
York  currency,  and  sold  the  same  at  5s.  per  bushel.  New 
England  currency.     IIow  much  did  I  gain  on  the  whole  ? 

6Q.  What  is  the  value  of  a  field  15  ch.  75  1.  long,  and  12 
ch.  50  1.  wide,  at  864  per  acre  ? 

67.  The  popular  vote  for  president  in  1800  was  4080193; 
Lincoln  received  491295  more  votes  than  Douglas,  who  re-r 
ceived  527204  miore  than  Breckinridge;  and  Breckinridge 
received  257322  more  than  Bell.  How  many  did  each 
receive  1 


84  ARITHMETICxiL    EXAMPLES. 

68.  Reduce  |  of  J  of  45i  lb.  to  the  decimal  of  a  short  ton. 

09.  Suppose  the  Erie  canal  to  be  60  feet  wide,  and  6  feet 
deep,  how  many  miles  in  length  will  it  require  to  make  one 
cubic  mile  of  water  1 

70.  In  the  packing-yards  of  New  York  there  were,  Feb.  1, 
1864,  88180  bbl.  of  pork,  and  107643  bbl.  of  beef;  the  aver- 
age value  of  the  pork  per  barrel  was  $20,124  ;  of  the  beef, 
$14.75.     What  was  the  difference  in  their  entire  values? 

71.  There  is  a  house  40  feet  long,  and  each  side  of  the  roof 
is  20  feet  wide ;  allowing  each  shingle  to  be  4  inches  wide, 
and  18  inches  long,  and  to  lie  one-third  to  the  weather,  how 
many  half-thousand  bunches  will  be  required  to  cover  the 
roof? 

72.  riov/  many  bushels  of  grain  will  a  bin  contain  that  is 
7.5  ft.  long,  6.25  ft.  wide,  and  3.75  ft.  deep  ? 

73.  Tlie  difference  in  longitude  between  London  and  St. 
Louis  is  90°  20' ;  at  a  certain  time  each  day  it  is  as  much  past 
noon  in  London  as  it  lacks  of  noon  in  St.  Louis.  What  is  the 
time  in  St.  Louis  ? 

74.  At  what  time  between  8  and  9  o'clock  is  the  minute- 
hand  as  far  beyond  the  V  mark  as  the  hour-hand  is  beyond 
the  VIII  mark  ? 

75.  A  gentleman  having  $60,  paid  in  Boston  14s.  8d.  for  a 
hat,  18s.  6d.  for  a  vest,  and  $17,375  for  a  coat;  going  to  New 
York,  he  paid  $5.00  for  his  fare,  and  in  the  city  bought  10 
books  at  7s.  6d.  each  ;  gave  3s.  9d.  to  a  blind  man ;  and  paid 
17s.  3d.  hotel  bill.     How  much  money  had  he  left  ? 

76.  On  an  acre  of  ground  there  were  erected  21  buildings, 
occupying  on  an  average  3  sq.  rd.  112  sq.  ft.  8  sq.  in.  How 
much  of  the  acre  remained  unoccupied  ? 

77.  Colt's  Armory,  Hartford,  Conn.,  which  was  destroyed 
by  fire,  February  4,  1864,  was  insured  in  New  Haven  to  the 
amount  of  $20000,  which  was  -  the  insurance  in  Providence, 
and  ^  the  insurance  in  Springfield  ;  the  amount  insured  in 
these  three  cities  was  |  the  insurance  in  Llartford ;    and  the 


ARITHMETICAL    EXAMPLES.  85 

insurance  in  New  York  was  14  times  all  the  others.     How 
much  was  the  total  insurance  '? 

New  Ha  yen,  Feb.  1,  1864. 
78.  T.  M.  CuRTiss, 

Bought  of  Bishop  &  Brothers, 


450  lb.  A.  Sugar 

.     @ 

S  .12^ 

240   "   B.       "             .         . 

.     @ 

.111 

•320   "         Rice 

.     @ 

.101 

220   "        0.  J.  Coffee 

.     © 

.22^ 

30  boxes  Oranges 

.     © 

3.75 

16       "     Lemons 

.     ® 

3.37^ 

15       "     Raisins 

.     ® 

4.12^ 

was  the  amount  of  the  bill  ? 

79.  A  person  lived  in  Massachusetts  until  he  was  18  years 
8  mo.  24  da.  old  ;  in  New  York  \  as  long  ;  in  Pennsylvania 
I  as  long  as  in  New  York,  and  4  as  long  in  Tennessee  as  in 
Pennsylvania.     What  was  his  age  ? 

80.  If  14  casks  of  raisins,  each  weighing  125  lbs.,  be  carried 
6  miles  for  $6.25,  what  will  be  the  cost  of  carrying  56  casks, 
each  weighing  100  lbs.,  66  miles  ? 

81.  What  cost  .01975  of  a  ton  of  steel  at  20  cents  per 
pound  \ 

82.  A  vessel  setting  sail  from  Boston,  proceeded  in  a  south- 
easterly direction  for  18  days;  the  captain  then  took  an  ob- 
servation upon  the  sun,  and  found  the  local  time  at  the  ship's 
meridian  to  be  9  h.  53  min.  27.6  sec. ;  at  the  moment  of  the 
observation,  his  chronometer,  which  had  been  set  for  Boston 
tim.e,  showed  7  h.  17  m.  45  sec;  allowing  that  the  chronome- 
ter had  lost  2.52  sec.  per  day,  how  much  had  the  ship  changed 
its  longitude  ? 

83.  A  man  labors  for  $16|  per  month,  what  will  his  wages 
amount  to  for  7|  months  1 

84.  If  4  of  a  yard  of  cloth  cost  |  of  a  dollar,  what  is  the 
price  per  yard  1 


83  ARITHMETICAL    EXAMPLES. 

85.  Bought  300  bushels  of  wheat  in  New  Jersey  at  8s.  per 
bushel,  and  sold  the  same  in  New  York  at  8s.  6d.  per  bushel. 
How  much  did  I  lose] 

8G.  From  |  of  305 j  da.,  and  |  of  5  J  wk.,  take  |  of  85-  min. 

87.  In  1863  the  imports  of  sperm  oil  were  G5055  gal. ;  of 
whale  oil,  62974  gal. ;  of  whalebone,  488750  lb. ;  the  average 
price  per  gallon  of  the  sperm  oil  was  C^l.OH;  of  the  whale 
oil,  $.95j,  and  of  the  whalebone,  11.52  per  pound.  What 
was  the  total  value  of  the  whaling  business  for  the  year  1 

88.  A  man  having  a  field  30  rods  square,  sold  25  square 
rods  to  one  of  his  neighbors,  and  20  rods  square  to  another. 
What  is  the  value  of  the  remainder  at  $175  per  acre? 

89.  If  corn  be  rated  at  7s.  6d.  per  bushel  in  Maine,  at  what 
price  in  the  currency  of  New  Jersey  must  it  be  sold  to  gain 
$13.50  on  90  bushels? 

90.  A  grocer  bought  15  bbl.  of  dried  cherries,  each  barrel 
containing  3  bushels,  at  $6  per  barrel,  and  directed  his  clerk 
to  retail  them  at  10  cents  a  quart.  By  mistake  he  used  a 
beer  measure.  IIow  much  did  the  grocer  lose  by  this  mis- 
take? 

91.  What  part  of  a  leap  year  is  past  at  noon  on  the  ^Fourth 
of  July  ? 

92.  How  many  bales  of  cotton,  of  400  lb.  each,  at  36  cents 
per  lb.,  are  equal  in  value  to  18  hhd.  of  sugar  of  1500  lb. 
each,  at  8  cents  per  pound  ? 

93.  There  is  a  park  300  feet  square ;  if  a  walk  4  feet  wide 
be  made  around  it,  within  the  inclosure,  how  many  square 
yards  will  it  contain  ? 

94.  If  a  gallon  of  distilled  water  weigh  8  lb.  5  oz.  6.74  dr., 
what  is  the  weight  of  17  gal.  3  qt.  1  pt.  1  gi.  ? 

95.  If,  when  wheat  is  worth  6s.  3d.  per  bushel,  a  5-cent  loaf 
weighs  24  oz.,  and  allows  the  baker  1 A  cents  a  loaf  for  his  lubor, 
what  should  it  weigh  when  wheat  is  8s.  4d.  per  bushel,  to 
afford  him  the  same  profit  on  a  loaf? 


AKITHMETICAL    EXAMPLES.  87 

96.  The  distributing  reservoir  of  Croton  water  is  425  feet 
square  on  the  top,  and  45  feet  high.  If  the  walls  were  perpen- 
dicular, what  would  be  its  capacity  in  wine  gallons  ? 

97.  At  3^  cents  per  foot,  what  will  be  the  cost  of  12  planks, 
each  measuring  56  ft.  9'  ? 

98.  There  is  a  garden  6  rods  long  and  5  rods  wide,  with  a 
ditch  around  it  5  ft.  wide  and  6\  ft.  deep,  the  earth  from 
which  was  thrown  upon  the  garden  in  uniform  thickness. 
How  much  was  the  surface  elevated '? 

99.  In  the  battle  of  Antietam,  the  number  killed  in  the 
Union  army  was  101  less  than  i  the  whole  loss;  the  prisoners 
were  35  more  than  A  the  killed,  and  the  wounded  were  144 
less  than  3i  times  the  sum  of  the  killed  and  prisoners.  What 
was  the  total  loss  ? 

100.  In  the  same  battle  it  w\as  estimated  that  the  number 
killed  in  the  rebel  army  was  equal  to  the  number  taken 
prisoners;  and  the  sum  of  these  was  ||  of  the  wounded;  the 
total  rebel  loss  was  1932  less  than  twice  the  Union  loss. 
What  was  the  number  killed,  wounded  and  prisoners  ] 

101.  Divide  100  into  two  such  parts  that  one  shall  be  12| 
greater  than  che  other  1 

102.  A  man  paid  ^■>46.50  for  a  certain  pile  of  wood.  Meas- 
uring it  he  found  that  it  contained  5  Cd.  6  cd.  ft.,  12  cu.  ft. 
What  did  the  wood  cost  him  per  cord  ? 

103.  A  room  is  18  ft.  6  in.  long,  14  ft.  6  in.  wide,  and  9  ft. 
9  in.  high ;  there  are  four  windows  in  the  room,  each  6  ft. 
long  by  3  ft.  3  in.  wide,  and  two  doors,  each  G  ft.  9  in.  high 
by  2  ft.  10  in.  wide;  the  base  is  9  in.  wide.  What  will  be 
the  cost  of  plastering  the  room  at  $.15  per  square  yard  ? 

104.  An  estate  worth  £3680  is  to  be  divided  as  follows : 
The  widow  has  J  of  the  whole,  and  the  remainder  is  to  be 
equally  divided  among  6  children.  How  much  does  each 
child  receive  ] 

105.  If  6  lb.  of  tea  be  worth  14  lb.  of  coffee,  and  7  lb.  of 


88  ARITHMETICAL    EXAMPLES. 

coffee  be  worth  24  lb.  of  sugar,  how  many  pounds  of  tea  can 
be  bought  for  16  lb.  of  sugar  ? 

106.  A  person  was  commissioned  to  lay  out  equal  sums  in 
the  purchase  of  spelling  books,  grammars,  algebras  and  ge- 
ometries,  and  to  expend  as  little  money  as  possible ;  he  found 
spelling  books  at  $.124-  each,  grammars  at  $.37 J,  algebras  at 
$.87^,  and  geometries  of  two  styles  of  binding;  one  at  $1.10, 
the  other  at  $1.25,  of  which  he  imprudently  chose  the  chenper. 
How  much  money  was  thereby  unnecessarily  expended,  and 
how  many  more  books  than  was  necessary  did  he  purchase  1 

107.  A  blacksmith  bought  20  tons  of  iron  at  $80  per  ton; 
he  sold  6  T.  15  cwt.  3  qr.  9  lb.,  at  $.05  per  pound  ;  having 
made  3522  horse  shoes,  averaging  2  lb.  8  oz.  in  weight,  and 
sold  them  at  $.25  each,  he  disposed  of  the  remaining  iron  at 
$98  per  ton.     How  much  was  his  gain  ? 

108.  How  much  will  it  cost  to  carpet  a  room  21  ft.  long, 
15  ft.  wide,  with  carpeting  |  of  a  yard  wide,  at  $1.62^  per 
yd? 

109.  A  goldsmith  manuflictured  1  lb.  10  oz.  15  pvvt.  of 
gold,  which  cost  him  $16  per  oz.,  into  rings,  each  weighing  2 
pwt.  12  gr,,  which  he  sold  at  $3.12A  each.  How  much  did 
he  receive  for  his  labor  1 

110.  What  decimal  expression  is  equivalent  to 

^  +.62.1  +  1  of  J4  of 4-1.05? 

111.  Bought  12  T.  3  cwt.  2  qr.  20  lb.  of  sugar  at  $8.25  per 
cwt."     What  was  the  cost  ? 

112.  If  a  mail  could  walk  around  the  earth  in  4  yr.  137  da. 
15  h.  48  min.,  how  long  would  it  take  him  to  walk  one  de- 
gree, allowing  365]  days  to  a  year? 

113.  A  merchant  owned  ji  of  a  stock  of  goods;  |  of  the 
whole  stock  were  destroyed  by  fire,  and  y\-  of  the  remainder 
damaged  by  water.  How  much  did  the  merchant  lose,  pro- 
vided the  uninjured  goods  were  sold  at  cost,  for  $4200,  and 
the  damaged  at  half  the  cost  1 


ARITHMETICAL    EXAMPLES.  89 

114.  My  farm  consists  of  8  fields,  containing  4?  5?  IOt^^.. 
9,  22|,  17^9,  ISfo",  aod  12^2  acres,  respectively.  How  many 
acres  in  my  farm  ? 

1      Qf      _3 

115.  I  of -y-  of  what  number,  diminished  by  '^——^,  leaves 

116.  My  garden,  which  is  ISO  ft.  long,  and  130  ft.  vride,  is 
surrounded  by  a  tight-board  fence  51  ft.  high.  How  much 
will  it  cost  to  paint  the  fence  on  both  sides  at  8.12  per  square 
yard  ? 

117.  Bought  37  T.  15  cwt.  3  qr.  15  lb.  of  copperas,  at  $.04 
per  lb.  ;  sold  at  one  time  8  T.  12  cwt.  3  qr.  3  lb.  at  $.05  per 
lb. ;  at  another  time  14  T.  3  cwt.  2  qr.  20  lb.  at  8.06  per  lb. ; 
James  Bond  bought  \  the  remainder  at  8.06  per  lb. ;  and 
John  Gaines  \  of  what  still  remained  at  8.10  per  lb. ;  George 
Eoot,  ^vho  bought  the  residue  at  8.12  per  lb.,  becoming  a 
bankrupt,  paid  but  50  cents  on  a  dollar  of  his  debt.  What 
was  my  whole  gain  ] 

118.  A  farmer  has  16|  bushels  of  corn,  33^  bushels  of  rye, 
35 -/g  bushels  of  wheat ;  he  wishes  to  put  the  grain,  without 
mixing,  into  the  .largest  possible  bags,  of  equal  size.  Re- 
quired the  number  of  bags,  and  the  capacity  of  each. 

119.  A  man  bought  35  bushels  of  barley,  and  sold  the 
whole  for  8-30.  He  made  85.50  in  the  trade.  What  did  he 
give  per  bushel  ? 

120.  A  tailor  has  67|  yds.  of  cloth,  from  which  he  wishes 
to  cut  an  equal  number  of  coats,  pants,  and  vests.  What 
number  of  each  can  he  cut,  if  they  contain,  respectively,  3|, 
2|,  14  yards  1 

121.  Erom  the  annual  report  for  1863,  the  tolls  collected 
on  the  canals  of  New  York  for  that  year  were  as  follows : 
On  wood  and  lumber,  8715059;  on  animals,  888426;  on 
vegetable,  83012823;  on  other  form  products,  814114;  on 
manufactures,  8137107;    on  merchandise,  8137253;    and  on 


90  ARITHMETICAL    EXAMPLES. 

Other  articles  enough  to  make  the  whole  amount  $4645207. 
What  was  the  amount  collected  on  articles  not  specified  1 

122.  How  many  bricks,  8  in.  long,  4  in.  wide,  and  2 J  in. 
thick,  are  required  to  build  the  front  of  a  house  whose  wall  is 
30  ft.  long,  24  ft.  high,  and  2  ft.  thick,  allowing  the  doors  and 
windows  to  occupy  ^  the  surface  ? 

123.  A  merchant  purchased  in  Liverpool  34  bales  of  cloth 
for  £8  19s.  5d.  per  bale ;  he  disposed  of  the  cloth  at  Ha- 
vana for  212  cwt.  of  sugar,  at  £1  5s.  per  cwt.  What  bal- 
ance was  due  him  in  cash  ? 

124.  A  company  of  36  persons  purchased  a  tract  of  land 
containing  2706  A.  3  R.  12  P. ;  J.  Jenks,  who  was  one  of  the 
company,  and  owned  an  equal  share  with  the  others,  sold  |  of 
his  part  for  Is.  9d.  2  far.  per  sq.  rd.  What  sum  did  he 
receive  ? 

125.  How  many  silver  dollars,  each  weighing  41 2 J  grains, 
could  be  made  from  the  silver  taken  at  the  doors  of  the  great 
London  exhibition,  the  weight  of  the  silver  being  35  English 
tons? 

126.  During  the  last  half  of  the  year  1863  there  were  189 
fires  in  the  city  of  New  York,  and  the  average  loss  by  each 
fire  was  '^2238.40;  the  insurances  amounted  to  5||  times  the 
losses,  and  the  amount  paid  by  the  underwriters  was  $38307-- 
.50  less  than  4  the  amount  of  insurance.  How  much  was 
the  actual  loss  ? 

127.  What  is  the  value  of  a  pile  of  wood  that  is  10  rods 
long,  4  feet  wide,  and  1  ^  yards  high,  at  $5.75  per  cord  ? 

128.  If  a  person  spends  in  6  months  what  he  earns  in  4A 
months ;  how  many  dollars  can  he  lay  by  in  a  year,  suppos- 
ing he  earns  $325  in  2A  months  ? 

129.  A  man  has  two  kinds  of  flour ;  the  first  is  worth  $2.50 
per  barrel  more  than  the  second,  and  9  barrels  of  the  second 
are  worth  as  much  as  7  of  the  first.  What  is  the  price  of 
each  per  barrel '? 


ARITHMETICAL   EXAMPLES.  91 

130.  What  part  of  3G5J  days  are  349  da.  8  h.  52  m.  lO^Q 
sec.  I 

131.  The  Connecticut  river,  which  is  60  rd.  10  ft.  wide  at 
a  certain  place,  has  an  average  depth  of  10  ft.,  and  runs  at  the 
rate  of  3|  miles  per  hour.  Li  what  time  will  it  discharge  a 
cubic  mile  of  water  ] 

132.  If  a  man's  property  is  worth  $1500,  and  he  owes 
$1800 ;  how  many  cents  can  he  pay  on  the  dollar  ? 

133.  If  a  man  can  pay  his  creditors  only  48  cents  on  a  dol- 
lar, how  much  can  he  pay  on  a  debt  of  S52.50 1 

134.  A  boy,  having  been  sent  to  market  to  buy  a  certain 
number  of  pounds  of  meat,  found  that  if  he  bought  beef  at 
10|  cents  a  pound,  he  would  have  6 A  cents  remaining ;  but  if 
he  bought  pork  at  13 "J  cents  a  pound,  he  would  lack  46  cents 
of  having  money  enough  to  pay  for  it.  How  much  money 
had  he  1  and  how  many  pounds  was  he  directed  to  buy  ? 

135.  A  farmer  wishes  to  build  a  bin  8  ft.  long,  6  ft.  wide, 
and  high  enough  to  hold  200  bushels  of  corn.  How  high 
must  he  build  it  1 

136.  How  long  from  the  Declaration  of  Independence,  July 
4,  1776,  to  the  firing  upon  Fort  Sumter,  April  12,  1861 1 

137.  The  value  of  the  products  of  Massachusetts  in  1860, 
with  a  population  of  1231065,  was  1289300275  ;  of  Mary- 
land, with  a  population  of  6S7034,  165955264.  How  much 
more  per  capita,  was  the  value  of  the  annual  products  of  the 
former  than  the  latter  State  ? 

138.  The  total  population  of  the  Slave  States  in  1860  was 
12229727 ;  allowing  the  average  annual  products  per  head  to 
have  been  the  same  as  in  Maryland,  how  much  would  the 
value  of  the  products  of  the  Southern  States  have  been  in- 
creased had  the  ratio  of  production  been  the  same  as  in  Mas- 
sachusetts 1 

139.  How  many  bushels  of  coal  will  a  boat  90  ft.  long,  42 


92  AKITHMETICAL    EXAMPLES. 

ft.  wide,  and  5^  ft.  deep  contain,  a  bushel  of  coal  being  IJ  cu. 
feet] 

140.  A  person  having  |  of  a  hogshead  of  wine,  sold  at  one 
time  I  of  a  gallon,  at  another,  J  of  a  quart.  How  many 
gallons,  expressed  decimally,  did  he  sell,  and  how  much 
remained  1 

141.  How  many  seconds  has  a  person  lived  M^ho  is  32  yr. 
197  d.i.  old,  allowing  for  8  leap  years  1 

142.  Paid  3  debts  successively,  each  of  which  took  i  the 
money  1  had  before  paying  it,  and  |.75  more  ;  after  which  I 
had  125  remaining.     How  much  had  I  at  first  ? 

143.  A  man  in  Ohio  bought  .82]-  of  a  firkin  of  butter  at 
$.28  per  pound;  .857|  bushels  of  corn  at  $.01 1  per  pound; 
.783]  bushels  of  wheat  at  1. 03 A  per  pound.  What  was  the 
amount  of  his  bill  ? 

144.  What  would  be  the  expense  of  paper  for  a  room  15 
ft.  9  in.  long,  14  ft.  6  in.  wide,  and  10  ft.  3  in.  high,  which 
contains  3  windows,  each  6  ft.  2  in.  long,  3  ft.  10  in.  wide, 
and  2  doors,  each  6  ft.  10  in.  by  3  ft.,  a  roll  of  paper  being  8 
yds.  in  length,  and  |  yd.  in.width,  and  costing  $.02^  "? 

145.  If  I  buy  120  gallons  of  rum  for  $75,  how  much  water 
must  be  added  to  it  that  I  may  sell  it  at  GO  cents  per  gallon, 
and  gain  $15  in  the  sale  of  it  1 

146.  Of  the  poor  people  assisted  by  the  State  of  New 
York  in  1863,  486  were  natives  of  Wales ;  52  less  than  4 
times  this  number  were  Canadians ;  and  the  Frenchmen  were 
140  less  than  3  times  the  same  number;  the  Scotch  were  270 
more  than  the  Canadians ;  the  English,  9  less  than  the  sura 
of  the  Welsh  and  twice  the  Scots ;  the  Germans  were  190  less 
than  4  times  the  English ;  and  the  Irish  were  64  more  than 
the  sum  of  the  Welsh,  twice  the  Canadians  and  5 A  times  the 
Germans;  the  native  born  were  7394  less  than  the  Irish,  and 
the  nationality  of  21151  was  unkiiovv'n.  Required  the  num- 
ber relieved. 

147.  The  whole  expense  for  the  support  of  the  poor  for  the 


ARITHMETICAL   EXAMPLES.  93 

same  year  was  Si 463 103.04.     What  was  the  average  amount 
expended  for  each  person  relieved  ? 

148.  What  are  the  contents  of  a  field  38 /^  rods  in  length 
and  S7h  rods  in  width? 

149.  Bought  a  barrel  of  flour  for  811.50;  4  bu.  corn,  at 
81.121 ;  26.25  lb.  sugar,  at  8  12A  ;  6  gal.  molasses,  at  8.62^  ; 
3  1b.  tea,  at  81.25;  9  lb.  coffee,  at  8.33 J ;  12A  lb.  rice,  at 
8.12^  ;  and  8  lb.  butter,  at  8.28.    What  did  the  whole  cost  ? 

150.  How  many  bricks  are  required  to  build  the  front  of 
a  house  50  ft.  8  in.  in  length,  15  ft.  8  in.  in  height,  and  1  ft.  6 
in.  in  thickness,  the  dimensions  of  a  brick  being  8,  4  and  2 
inches  ? 

151.  The  largest  bell  in  the  world  is  that  of  Moscow,  which 
weighs  192  tons  17  cwt.  16  lb. ;  the  great  bell  of  St.  Paul's 
weighs  5  tons  2  cwt.  1  qr.  22  lb.  How  many  bells  of  the 
latter  weight  could  be  made  from  the  former? 

152.  If  a  train  of  cars  move  with  an  average  velocity  of 
32  mi.  5  fur.  20  rd.  in  1  h.  20  min.,  how  far  will  it  move  in 
3  h.  36  min.  ? 

153.  What  are  the  prime  factors  of  1400  ? 

154.  How  many  integral  divisors  has  1400  ? 

155.  When  $207  are  paid  for  lO/g  months'  labor,  what 
wages. shall  be  paid  for  17 -^q  months'  work? 

156.  In  Webster's  Unabridged  Dictionary,  Pictorial  Edi- 
tion, there  are  1750  pages  of  three  columns  each,  and  in  each 
column  there  are  on  an  average  100  lines,  2^'^  inches  long. 
How  many  miles  of  lines  in  the  book  ? 

157.  There  are  on  an  average  45  letters  and  points  in  each 
line;  if  the  hand  moved  over  a  distance  of  3  feet  in  setting 
each  type,  how  far  did  the  compositor's  hand  travel  in  setting 
up  the  book? 

158.  If  a  compositor  worked  10  hours  each  day.  and  on  an 
average  set  50  types  in  a  minute,  when  would  he  have  finished 
setting  up  the  book,  provided  he  began  it  Jan.  1,  1856,  ob- 


94  ARITHMETICAL    EXAMPLES. 

served  the  Sabbath,  and  was  allowed  the  Fourth  of  July  and 
Thanksgiving  as  holidays  1 

159.  What  is  the  amount  of  the  following  bill : 

Cleveland,  Jan.  1,  1864. 
Mr.  Peter  Jones 

Bought  of  Samuel  Carter  &  Co. 


20  lb.  Rio  Coffee       . 

® 

$.40 

35  "    W.  India  Sugar       . 

@ 

"  .161 

24  "    Pearl  Starch 

@ 

^'.14 

C  gal.  Molasses 

© 

"•75 

75  lb.  Cream  Crackers 

® 

"  .11 

20  "    Soda          "    . 

© 

"    .10:1 

160.  Sold  125  equal  loads  of  wood,  measuring  115  Cd.  3 
cd.  ft.  7  cu.  ft.  for  $492.50.  What  is  the  quantity  per  load, 
and  price  per  cord  ? 

161.  Bought  14  lots  of  land,  each  containing  37  P.  200  sq. 
ft. ;  from  this  purchase  I  sold  2  A.  2  R.  25  P.  60  sq.  ft.,  and 
the  remainder  I  disposed  of  at  2s.  3H.  per  sq.  ft.  How  much 
did  I  receive  for  the  last  sale  ? 

162.  What  is  the  value  of  719630  pounds  of  wheat  at 
11.80  per  bushel? 

163.  How  many  half-dimes  would  it  take  to  pay  for  18 
doz.  of  eggs,  at  $.30  per  doz.  ? 

164.  A  flirmer,  having  harvested  his  crops,  finds  that' he  has 
corn  enough  to  fill  the  first  of  the  following  boxes ;  wheat 
enough  to  fill  the  second,  and  rye  enough  to  fill  the  third. 
The  outer  dimensions  of  the  boxes  are  as  follows :  of  the  first, 
10»  ft.  long,  6J  ft.  wide  and  6  ft.  high;  of  the  second,  9~  ft. 
long,  71  ft.  wide  and  5^  ft.  high;  of  the  third,  12  ft.  long,  10 
ft.  wide  and  7  ft.  high ;  they  are  made  of  plank  2  in.  thick. 
He  sells  the  corn  at  $.75  a  bushel,  the  wheat  at  $1.12A,  the 
rye  at  $.95.  Plow  many  bushels  of  21 50.5  cu.  in.  had  he  of  each 
kind  of  grain,  and  how  much  money  did  the  whole  bring  him? 

165.  A  man  has  a  field  37i  rods  wide.  What  length  must 
he  cut  off  from  the  end  to  set  off  5  A.  3  R.  25  P.  ? 


ARITHMETICAL   EXAMPLES.  95 

lOG.  The  Mississippi  River  flows  directly  south,  through 
19°  15'  of  latitude.  The  earth  is  an  oblate  spheroid,  and  the 
equatorial  diameter  is  13  miles  more  than  the  polar  diameter. 
How  much  farther  from  the  centre  of  the  earth  is  the  mouth 
of  the  river  than  its  source  1 

167.  The  above  river,  on  account  of  its  numerous  windings, 
is  3160  miles  long.  What  is  the  average  rise  of  the  river  per 
mile  ? 

168.  If  the  factors  of  a  certain  number  are  16],  30 f  and 
O^^o  ;  ^^hat  is  §  of  I  of  I  of  the  number? 

169.  Josephus  relates  that  the  battering  ram  employed  by 
Titus  against  the  walls  of  Jerusalem  weighed  100000  pounds. 
Now  if  his  men  could  move  it  with  a  velocity  of  6  ft.  a  sec- 
ond, how  many  cannon  balls  of  100  pounds  each,  discharged 
with  a  velocity  of  1200  ft.  a,  second,  would  be  necessary  to 
strike  the  walls  with  equal  force  ? 

170.  How  many  fi-ancs  must  a  merchant  in  Paris  send  to 
New  York  in  payment  for  a  debt  of  815989.862'? 

171.  I  have  a  field  96  rods  long  and  50  rods  wide.  How 
much  would  it  cost  to  build  a  fence  around  it,  at  8.12^  per 
foot? 

172.  Reduce  .18,  .369,  .307692  and  6.75  to  equivalent 
common  fractions. 

173.  Gen.  McClellan  estimated  the  rebel  forces  engaged  in 
the  battle  of  Antietani  as  follov»'s  :  Gen.  Jackson's  corps,  24- 
778  men  ;  Gen.  Longstrcet's,  1436  less  than  Gen.  Jackson's ; 
Gen.  Hill's,  15525;  Gen.  Stuart's  cavalry,  6400;  Gen.  Jen- 
kins',  200  more  than  -^  of  Gen.  Stuart's;  reserves,  18400,  and 
artillery  400  guns,  with  15  men  each.  What  was  the  esti- 
mate of  the  rebel  force  ? 

174.  Tlie  Union  army  in  the  same  battle  numbered  as  fol- 
lows :  1st  corps,  14856 ;  2d  corps,  18813  ;  5th  and  6th  corps, 
12615   men  each;  9th  corps,  13819;   12th  corps,  3693  less 
than  the  9th ;  and  the  cavalry  115  more  than  -]  the  5th  corps. ' 
AYhat  was  the  strength  of  the  Union  army  1 


96  ARITHMETICAL   EXAMPLES. 

175.  If  a  man  fill  ^  of  a  cask  with  brandy,  i  with  wine, 
and  I  with  water,  and  it  lack  21 J  gallons  of  being  full,  how 
many  gallons  will  that  cask  contain  ? 

176.  A  man,  having  ji  of  5  tons  of  iron,  sold  |  of  9  cwt. 
What  was  the  value  of  the  remainder  at  12f  cents  per 
pound  ] 

177.  Light  moves  192000  miles  per  second;  sound,  1142 
feet  per  second,  and  a  cannon  ball,  with  an  average  velocity 
of  800  feet  per  second.  If  a  ball  is  discharged  from  a  can- 
non 6  miles  distant  from  a  person,  how  long  after  the  flash 
is  seen  will  the  sound  reach  his  ear,  and  how  long  after  the 
sound  will  the  ball  arrive? 

178.  The  average  distance  of  the  planet  Neptune  from  the 
earth  is  2864000000  miles ;  should  it  be  blotted  out,  how 
long  thereafter  would  its  light  be  visible  from  the  earth,  the 
velocity  of  light  being  192000  miles  per  second? 

179.  Exchanged  .5  firkins  of  butter  of  50  lb.  each,  at  $,% 
per  pound,  for  50  bags  of  guano,  of  llGf  lb.  each.  What 
was  the  price  of  the  guano  per  short  ton  ? 

180.  What  weight  of  water  in  a  cistern  10  ft.  6  in.  square, 
and  8  ft.  4  in.  deep,  a  cubic  foot  of  water  weighing  1000 
ounces  ? 

181.  Great  Britain,  with  a  population  of  29334788,  had  in 
1861  a  national  debt  of  $3917945913,  the  annual  interest  of 
which  was  81276()5701.  What  was  the  average  debt  and 
•annual  interest  to  each  person  1 

182.  France,  with  a  population  estimated  at  3G000000,  had 
at  the  same  time  a  debt  of  $2206000000,  the  annual  interest 
of  which  was  $110000000.  What  was  the  average  debt  and 
interest  to  each  person  ? 

183.  AVhat  will  it  cost  to  construct  8  mi.  6  fur,  16  rd.  of 
plank  road  at  $1325.65  per  mile? 

184.  What  part  of  a  short  ton  is  f  of  a  long  ton  ? 

185.  How  much  copper  and  tin  in  the  great  bell  of  Mos- 


ARITHMETICAL   EXA3IPLES.  97 

COW,  which  weighs  192  tons  17  cwt.  16  lb.,  bell  metal  con- 
sisting of  3  parts  copper  to  1  of  tin  ? 

186.  A  gentleman  buys  2  lots  of  land  containing  110  acres 
each,  for  $1500.  What  is  the  value  of  an  acre  of  land  in 
each  lot,  if  an  acre  in  one  lot  be  worth  1  i  acres  in  the  other  ? 

187.  A  farmer  borrows  20  bushels  of  corn  when  it  is  56 
cents  per  bushel.  How  many  bushels  must  he  return  when 
it  is  worth  75  cents  a  bushel,  to  pay  the  value  of  what  h& 
borrowed  1 

188.  The  army  of  Gen.  Banks  in  its  retreat  down  the  Shen- 
andoah Valley,  May,  1862,  marched  37^  miles  in  11  h.  24 
min.  26 1  sec.  How  many  steps  of  2  ft.  8  in.  each  did  his 
men  take  per  minute  ? 

189.  What  number  multiplied  by  3  J  times  itself  will  pro- 
duce 1141 

190.  Bought  425.75  lbs.  wool  at  $.75  per  lb.,  which  was 
manufactured  into  cloth  at  an  expense  of  $75.50.  For  how 
much  must  it  be  sold  to  gain  $48.25 1 

191.  How  many  feet  of  boards  will  be  required  to  make  8 
boxes,  whose  interior  dimensions  are  6  ft.  5  in.,  5  ft.  7  in.,  and 

3  ft.  6  in.  respectively,  the  boards  being  1^  in.  in  thickness"? 

192.  How  many  feet  less  are  required  to  make  8  boxes 
whose  exterior  dimensions  are  like  the  interior  of  those  in  the 
last  example,  the  boards  being  of  the  same  thickness? 

193.  What  is  the  difference  in  the  capacity  of  the  two  sets 
of  boxes? 

194.  There  were  sold  in  New  York,  in  one  week,  4678 
beeves,  156  cows,  367  veals,  12281  sheep  and  lambs,  and 
6297  swine.  The  average  price  of  the  beeves  was  $80  per 
head;  the  cows,  $44.25;  the  veals,  $12.50;  the  sheep  and 
lambs,  $7.50,  and  swine,  $18.25.  What  was  the  whole  num- 
ber of  animals  sold,  and  for  how  much  ? 

195.  A  merchant  bought  18  hogsheads  of  sugar,  each  con- 
taining .725  of  a  long  ton,  at  the  rate  of  $170  per  ton,  and 

5 


98  ARITHMETICAL    EXAMPLES. 

sold  the  same  at  10  cents  per  pound.     TIow  much  was  his^ 
gain  1 

196.  Y.  r.  Smith  has  coffee  at  1.37^  per  pound  cash,  but 
in  trading  with  Seth  Bishop,  he  charges  $.42.  What  must 
Bishop  charge  him  for  potatoes  that  he  sells  at  S.62A  cash? 

197.  On  J  of  my  field  I  raise  tobacco;  on  |  of  the  remain- 
der I  sow  oats;  potatoes  are  planted  on  ^  of  what  still  re- 
mains, and  carrots  on  ^  of  the  residue ;  I  have  left  two  small 
pieces,  one  of  which  is  4  rods  square,  and  the  other  contains 
4  square  rods.     How  large  is  my  field  1 

198.  There  were  4419216  bales  of  cotton,  each  400  lbs., 
exported  from  the  United  States  in  1 8 GO,  at  an  average  price 

^of  $.108  per  pound,  and  167248  hogsheads  of  tobacco  at 
195.12.1  per  hogshead.  What  was  the  value  of  cotton  and 
tobacco  exported  1 

199.  If  by  selling  cloth  at  10s.  6d.,  |  of  the  price  is  gain, 
what  part  of  the  cost  would  be  gained  by  selling  it  at  13  shil- 
lings 1 

200.  From  10  years  subtract  9  yr.  9  mo.  9  wk.  9  da.  9  h. 
9  min.  9  sec. 

201.  A  merchant  bought  15  barrels  of  salt,  of  4  bushels 
each,  at  $1|  a  barrel,  and  retailed  it  at  §  of  a  cent  a  pint. 
How  much  was  his  whole  gain  ? 

202.  The  Pennsylvania  Central  Railroad  is  356  miles  long : 
4  passenger  trains  and  six  freight  trains  pass  over  it  both 
ways  each  day  of  the  year,  Sundays  excepted.  How  many 
males  do  the  trains  run  each  year  '?  and  how  many  times  the 
circumference  of  the  earth,  which  is  about  25000  miles'? 

203.  A  ship's  chronometer,  set  at  Greenwich,  points  to  5  h. 
45  min.  24  sec.  P.  M.,  when  the  sun  is  on  the  meridian. 
What  is  the  ship's  longitude  ? 

204.  Bought  7.88125  A.  of  land  at  J^  of  £2  lis.  6d.,  New 
England  currency,  per  square  rod.  How  many  dollars  did  it 
cost? 


ARITHMETICAL    EXAMPLES.  99 

205.  The  salary  of  the  President  of  the  United  States  is 
$25000  jpjer  annum.  How  much  can  he  spend  each  week, 
and  yet  save  827200  in  one  term  of  office  1 

208.  Eequired  the  quotients  of  1169  divided  by  its  two 
prime  factors  next  larger  than  1. 

207.  A  farmer  bought  some  oxen,  cows,  and  sheep  for 
^1800,  paying  $45,  $25,  and  $4  per  head,  respectively. 
There  were  5  times  as  many  cows  as  oxen,  and  7  times  as 
many  sheep  as  cows.     How  many  of  each  did  he  purchase  1 

208.  A  owns  Y'3  of  a  field,  and  B  the  remainder ;  |  of  the 
difference  between  their  shares  is  5  A.  3  R.  IGi  P.  What  is 
B's  share  1 

209.  The  average  fall  of  rain  at  Worcester,  Mass.,  is  48.92 
in. ;  of  snow  53.5  in. ;  allowing  5  in.  of  snow  to  make  one  of 
rain,  how  many  hogsheads  of  water  fall  annually  upon  a  flat 
roof  40  ft.  long  by  30  wade  1 

210.  A  wine  merchant  wished  twice  as  many  quart  bottles 
as  pint ;  twice  as  many  pint  as  half-pint,  and  twice  as  many 
half-pint  as  gill  bottles  filled  from  a  cask  of  wine  containing 
58  gal.  1  qt.  1  pt.  2  gi.  How  many  bottles  of  each  kind 
could  he  fill  ? 

211.  Peter  Jones  was  born  Sept.  7,  1830 ;  he  was  27  yr. 
3  mo.  23  da.  old  when  married ;  and  3  yr.  21  da.  after  mar- 
riage his  first  child  was  born.  What  was  the  date  of  his  mar- 
riage 1  and  w^hat  his  child's  birth-day  ? 

212.  How  much  more  is  the  cost  of  39  A.  2  R.  15  P.  of 
land  at  887.375  per  acre,  than  the  expense  of  making  5  mi.  6 
fur.  24  rd.  of  road  at  8587.75  per  mile? 

213.  There  werQ  shipped  over  the  Erie  Canal  in  1863 
1603065  barrels  of  flour,  22336433  bushels  of  wheat,  19918- 
464  bushels  of  corn,  and  3816548  bushels  of  barley ;  the  toll 
for  the  flour  was  8.375  per  barrel,  and  for  the  grain  8.075  per 
bushel ;  oats  were  shipped  in  such  a  quantity  that  the  tolls 
from   the   oats,  barley,   and   corn   were    equal    to  the   tolls 


100  ~  ARITHMETICAL    EXAMPLES. 

from  tlie  flour  and  wheat.     Plow  many  bushels  of  oats  were 
shipped  ?  ^^ 

214.  Two  boys  purchased  a  pair  of  skates  in  company; 
one  paid  $J,  and  the  other  $l/(j;  they  sold  them  so  as  to 
gain  $/g.  What  did  they  sell  them  for  ?  and  how  much  was 
each  one's  share  of  the  gain  1 

215.  How  long  before  the  voting  is  ended  in  San  Francis- 
co, Lon.  122°  13'  W.,  can  the  voters  of  Eastport,  Me.,  Lon. 
67°  W.,  telegraph  to  San  Francisco  the  result  of  their  election, 
the  polls  closing  in  both  places  at  sunset  1 

210.  At  what  time  between  11  and  12  o'clock  is  the  min- 
ute-hand as  far  beyond  the  XI  as  the  hour-hand  lacks  of  being 
up  to  the  XII  mark  ? 

217.  A  man  started  from  Portland,  Maine,  with  $100;  he 
paid  ^3.25  for  his  fare  to  Boston ;  in  that  city  he  bought  a 
book  for  5s.  6d.,  paid  8s.  3d.  hotel  bill  and  3s.  3d.  for  amuse- 
ments; he  then  took  passage  in  a  steamer  for  Charleston, 
S.  C,  paying  $32;  in  tliat  city  he  purchased  8  yards  of  cloth  at 
13s.  6d.  per  yard,  and  paid  18s.  9d.  for  having  the  cloth  made 
up;  he  then  went  to  Philadelphia,  at  an  cxnenso  of  $25,  and 
there  he  purchased  some  fjctures  for  15s.  lid.,  some  present  i 
for  IBs.  5d.,  and  spent  17s.  8d.  at  a  hotel ;  the  C'amden  and 
Amboy  Railroad  Company  agreed  to  carry  him  to  I'Tcv/  York 
for  the  rest  of  his  money  ;  the  regular  fare  being  $3.00,  how 
much  did  the  company  lose  1 

218.  At  $1000  per  acre,  what  is  the  value  of  a  strip  of  land 
44  yards  long  and  20  feet  wide  1 

219.  The  value  of  exports  from  the  United  States,  in  18G1, 
was  as  follows:  the  products  of  the  sea,  $4451515 ;  of  the 
forest,  $10260809;  of  agriculture,  $101655833;  tobr.cco, 
$13784710;  cotton,  $34051483;  manufactures,  $36418254; 
raw  produce,  $3543695 ;  specie  and  buliion,  $23799870. 
How  much  did  the  exports  of  the  products  of  agriculture  and 
manufacture  exceed  all  others  in  value '? 

220.  The  hour  and  minute  hands  of  a  clock  being  together 


ARITHMETICAL   EXAMPLES.  101 

at  12  o'clock,  how  long   before   they  will  be  at  right  angles 
with  each  other  ? 

221.  A  cistern  has  three  receiving  and  three  discharging 
pipes ;  the  first  three  will  fill  it  in  24,  36  and  48  minutes  re- 
spectively, and  the  last  three  will  empty  it  in  30,  40  and  60 
minutes  each.  If  the  cistern  is  empty,  and  the  pipes  are 
opened  in  succession,  each  three  minutes  after  the  other,  in 
the  order  given,  how  long  after  the  last  pipe  is  opened  will 
the  cistern  be  filled  ? 

222.  By  selling  wheat  at  12s.  6d.  per  bushel,  I  gain  £30  on 
the  quantity  purchased ;  but  if  I  sell  it  for  13s.  6d.  a  bushel, 
I  shall  gain  £42  on  the  same  quantity.  How  many  bushels 
were  bought  1 

223.  I  had  J  of  a  yard  of  broadcloth,  for  which  I  paid  at 
the  rate  of  881  per  yard  ;  I  gave  the  broadcloth  and  50  cents 
for  li  yards  of  cassim.ere.  What  did  the  cassimere  cost  me 
per  yard  1 

224.  A  liquor  agent  has  50  gallons  of  wine  of  a  superior 
quality,  worth  $7.50  a  gallon ;  he  wishes  to  reduce  its  quality 
by  tho  addition  of  water,  so  that  he  may  sell  it  at  85.25  a 
gallon.     How  much  water  must  he  add  ? 

".  225.  The  loans  of  all  the  banks  in  the  city  of  New  York, 
for  two  succe33ive  years,  were:  for  the  first,  8165090329; 
for  the  second,  8168302935,  The  deposits  for  the  same  pe- 
riods were  8140464616  and  8148014106  respectively.  How 
much  did  the  increase  of  deposits  exceed  that  of  loans  1 

226.  William  Shakspeare  was  born  April  23,  1564.  How 
many  years  since  ? 

227.  A  man  and  a  boy  start  from  the  same  place  at  the 
same  time,  and  travel  in  the  same  direction ;  the  man  ad- 
vances as  flxr  in  three  steps  as  the  boy  in  five,  but  the  boy 
takes  4  steps  while  the  man  takes  3 ;  after  a  certain  time 
they  are  1  mile  apart.  Allowing  the  man's  steps  to  be  3  feet 
in  length,  how  far  has  each  traveled  ? 

228.  If  1  cubic  foot  of  water  weigh  .625  cwt.,  what  will  be 


102  ARITHMETICAL   EXAMPLES. 

the  weight  of  water  in  a  cistern  containing  500  cu.  ft.  864 
cu.  in.  ? 

229.  What  are  the  values  of  a  bushel  of  peas,  sold  at  10 
cents  a  quart,  by  wine,  beer  and  dry  measure,  respectively  ? 

230.  The  total  loss  of  the  Federal  army  in  the  battle  of 
Fair  Oaks  was  5739 ;  the  prisoners  were  332  more  than  the 
killed,  and  the  wounded  were  459  more  than  U  times  both 
the  killed  and  prisoners.     What  were  the  various  losses  ? 

231.  What  is  the  cost  of  a  great  gross  of  pens,  at  Gj  cents 
for  J  of  a  dozen  ? 

232.  A  person  desirous  of  giving  Is.  6d.  apiece  to  some  needy 
boys,  found  that  he  had  not  money  enough  in  his  pocket  by 
5d. ;  he  therefore  gave  them  each  Is.  4d.,  and  had  9d.  left. 
Required  the  number  of  boys. 

233.  A  housewife  exchanged  old  silver  for  a  feather  bed 
worth  124 ;  the  feathers  were  valued  at  $.80  a  pound,  and 
the  silver  at  25  times  the  value  of  its  own  weight  of  feathers. 
What  was  the  Troy  weight  of  the  silver  1 

234.  If  a  man  can  paint  4  sq.  yd.  in  one  hour,  and  is  31  h. 
6  min.  40  sec.  in  painting  two  sides  of  a  wall  7  feet  high,  how 
long  is  the  wall  ? 

235.  The  earth  moves  through  59  .14 'daily,  how  far  did  it 
move  during  the  month  of  February,  1864? 

236.  The  average  cost  of  the  school  houses  in  Ohio,  in 
1861,  was  $289.20.  The  total  cost  of  the  same  was  $4794- 
357.60.     Required  the  number. 

237.  The  value  of  the  common  school  libraries  at  the  same 
time  w^as  $233499.76 ;  the  books  were  worth  on  an  average 
$.68  each,  and  were  distributed  in  libraries  averaging  47 
vols.  each.     Required  the  number  of  libraries. 

238.  In  the  same  state  27106  teachers  were  examined  dur- 
ing the  year  1861  ;  three  times  the  number  rejected  were  934 
more  than  the  number  considered  qualified  to  teach.  How 
many  passed  examination,  and  how  many  were  rejected  1 


ARITHMETICAL   EXAMPLES.  103 

239.  A  person  bought  a  watch,  chain  and  pencil,  for  £30  ;  the 
chain  cost  twice  as  much  as  the  pencil,  and  the  watch  twice 
as  much  as  the  chain  and  pencil.     AVhat  did  ho  give  for  each  1 

240.  If  I  exchange  4  bu.  lA  pk.  of  potatoes  for  2  bu.  2  pk. 
of  apples ;  how  many  bushels  of  apples  ought  I  to  receive  in 
exchange  for  33  bu.  1  pk.  of  potatoes  at  the  same  rate  ] 

241.  A  man  chopping  wood  at  $.75  per  cord,  earned  ^35.25 
during  the  working  days  of  January,  1864,  and  was  idle  2J 
days.     How  much  wood  did  he  cut,  on  an  average,  per  day  ? 

242.  A  boy  having  been  sent  to  the  store  with  5,^  doz.  of 
eggs,  was  directed  to  purchase  with  them  equal  quantities  of 
sugar,  coffee,  butter  and  tea ;  he  disposed  of  his  eg<^s  at  the 
rate  of  2  for  5  cents,  and  paid  for  the  articles  purchased  IT, 
28,  37 ;l  and  137 A  cents  per  pound  respectively.  What 
amount  of  each  did  he  purchase  1 

243.  A  bowlder,  containing  §  of  g  of  23^  cu.  ft.,  is  what 
fraction  of  a  perch  1 

244.  A  grocer  bought  10  bushels  of  beans  at  83  per  bushel, 
and  ordered  his  shop  boy  to  retail  them  at  15  cents  a  quart. 
By  mistake  the  boy  used  a  wine  quart.  How  much  more  was 
the  grocer's  gain  than  he  expected  1 

245.  What  part  of  12  yd.  1  ft.  6  in.  is  rryij-,  of  a  mile? 

246.  Four  men  receive  827.27  for  hauling  coal  ;  the  first 
hauled  2  T.  3  cwt.  3  qr.  18  lb. ;  the  second,  5  T.  16  cwt.  7  lb.; 
the  third,  4  T.,  18  cwt.  2  qr.;  the  fourth,  14  cwt.  20  lb. 
How  must  the  money  be  divided  1 

247.  What  is  the  difference  in  weight  between  8  lb.  of  gold 
and  8  lb.  of  lead? 

248.  A  speculator  purchased  10,000  bushels  of  corn  in 
Chicago,  at  5s.  6d.  per  bushel,  and  sold  one-half  of  it  in  New 
Jersey  at  8s.  4d.  |)er  bushel,  and  the  other  half  in  New  York 
at  9s.  6d.  per  bushel;  the  freight  was  1.10  a  bushel,  and  other 
charges  amounted  to  8230.  The  corn  being  bought  and  sold 
by  weight,  how  much  did  he  gain  1 


104  ARITHMETICAL    EXAMPLES. 

249.  My  garden  is  10|  rods  long,  and  8g  rods  wide,  and 
surrounded  by  a  fence  7|  feet  high ;  I  have  laid  out  a  walk 
around  it,  within  the  fence,  71  feet  wide  on  the  two  sides,  and 
5:^  feet  wide  on  the  ends.  How  much  remains  for  cultiva- 
tion 1 

250.  What  part  of  a  cord  of  wood  is  a  load  71-  ft.  long,  2i 
ft.  high,  31  ft.  wide? 

251.  It  is  estimated  that  England  uses  annually,  1000000 
pounds  of  ivory.  The  average  product  of  ivory  from  each 
elephant  is  120  To. ;  and  for  every  25  elephants  captured  12 
men  are  killed.  Required  the  number  cf  men  killed  annually 
in  hunting  the  elephants  that  supply  England  with  ivory  1 

252.  How  many  dollars,  Canada  currency,  are  equal  to 
$150  United  States  currency] 

253.  If  j\  of  an  acre  produce  28  bushels  of  potatoes,  how 
many  bushels  will  4  acres  produce,  at  the  same  rate  ? 

254.  Bought  78  A.  3  R.  15  P.  7  sq.  yd.  5  sq.  ft.  9  sq.  in., 
at  $80  per  acre ;  I  sold  |  of  it  to  A,  at  $120  per  acre ;  |  of 
the  remainder  to  B,  at  11.00  per  square  rod  ;  and  the  residue 
to  C,  at  $.005  per  square  foot.     How  much  did  I  gain  ? 

255.  How  thick  is  a  cubic  inch  of  gold,  beaten  so  as  to  cover 
a  space  83  ft.  4  in.  long  and  and  23  ft.  5  in.  wide  ? 

256.  During  1861,  the  Dead  Letter  Post  Office  sent  out 
for  delivery  10580  money  letters,  and  10235  letters  contain- 
ing other  articles  of  value  ;  8998  of  the  former  and  9552  of 
the  latter  were  delivered ;  1214  money  letters  and  475  others 
were  returned,  unclaimed  ;  and  nothing  was  heard  from  the 
rest.     How  many  were  unreported  ? 

257.  The  money  letters  contained  $53565.90,  of  which  $46- 
880.26  was  delivered,  and  $4782.99  was  returned ;  of  the  re- 
mainder, $297.30  belonged  in  the  loyal  States,  and  the  rest  in 
the  disloyal.     What  amount  belonged  in  the  rebel  States  ? 

258.  At  $3.87^  per  square,  what  will  be  the  expense  of 
flooring  a  house  in  v/hich  there  are  4  rooms,  14  ft.  6  in.  by  15 


ARITHMETICAL    EXAMPLES.  105 

ft.  3  in. ;  G  rooms  9  ft.  9  m.  by  11  ft.  4  in.,  and  3  rooms  12 
ft.  3  in.  by  8  ft.  2  in.  ? 

259.  What  is  the  value  of  ^g  Cong.  1 

260.  Bought  1500  bushels  of  oats  in  Iowa,  at  8.40  a  bushel. 
For  how  much  per  bushel  must  I  sell  them  in  Connecticut,  so 
that,  after  paying  $75  expenses,  I  shall  neither  gain  nor  lose  by 
the  transaction,  the  buying  and  selling  being  by  weight  ? 

261.  Bought  140  yards  of  cloth  at  14s.  8d.  a  yard,  New 
York  currency,  and  gave  in  payment  75  bushels  of  barley  at 
7s.  4d.,  New  England  currency,  and  100  bushels  of  oats  at 
6s.  9d.  per  bushel.  New  Jersey  currency,  and  the  balance  in 
money.     How  much  money  did  I  pay  ? 

262.  A  steamer,  going  from  New  York  to  Hamburg,  trav- 
ersed 10.1  degrees  of  longitude  daily.  What  length  of  time 
was  it  from  one  noon  to  the  nexf? 

263.  A  certain  number  is  divided  by  9,  and  the  quotient 
multiplied  by  17 ;  the  product  is  then  divided  by  300,  and 
33  is  added  to  the  quotient ;  the  result  is  next  divided  by  3, 
and  from  this  quotient  31  is  subtracted,  and  the  resulting  dif- 
ference divided  by  12^.  Now  A  of  f  of  |  of  this  last  quotient 
is  2f^.     Required  the  original  number. 

264.  What  is  the  a*'uo  in  statute  miles  of  -^rr  of  a  Great 
Ch'cle  of  the  earth  ? 

265.  The  military  expenses  of  England,  during  the  last  war 
with  the  United  States,  were  as  follows:  for  1811,  £52859- 
025;  for  1812,  £56615577 ;  for  1813,  £71316435 ;  and  for 
1814,  £71686706.  A  pound  being  valued  at  84.84,  what 
were  the  average  daily  expenses  in  U.  S.  currency  1 

266.  A  clothier  has  920  soldiers'  coats  to  make,  each  coat 
containing  2|  yd.  of  cloth  IJ  yd.  v.ide,  and  lined  with  drilling 
I  yd.  wide.     How  many  yards  of  lining  will  be  required  ? 

•  267.  Reduce  f  -1  of  a  long  ton  to  the  decimal  of  a  short  ton. 

268.  Two  persons  traveling  in  the  same  direction,  the  first 

at  the  rate  of  9|  miles  per  hour,  the  second  14^  miles,  pass 


106  ARITHMETICAL    EXAMPLES. 

the  same  mile-stone  at  an  interval  of  5  hours.  How  long  and 
how  fir  must  the  second  travel,  after  passing  the  m.ile-stone, 
to  overtake  the  first  ? 

2G0.  What  is  the  length  of  the  shortest  piece  of  cloth  from 
which  a  number  of  garments  can  be  cut,  without  waste,  con- 
taining a  yard,  an  ell  Flemish,  an  ell  English,  and  an  ell 
French,  respectively  ? 

270.  The  shadow  of  a  cloud  was  observed  to  move  600  ft. 
in  23|  sec.     What  was  the  wind's  velocity  per  hour  1 

271.  From  1838  to  1863,  3858  patients  were  admitted  into 
the  Central  Lunatic  Asylum,  Ohio  ;  of  these,  2000  were  dis- 
charged as  fully  recovered,  412  as  improved,  724  as  incurable, 
and  470  died.  How  many  remained  in  the  asylum,  Jan.  1, 
1863? 

272.  A  gentleman  bought  95  yards  of  cloth,  |  of  a  yard 
wide,  for  $100,  and  gave  the  same  and  $25  for  cloth  of  the 
same  quality,  1  yard  wide.     How  many  yards  did  he  buy  1 

273.  If  a  vessel  sail  80  leagues  in  a  day,  how  many  statute 
miles  docs  she  sail  ? 

274.  A  farmer  exchanged  1 1  loads  of  potatoes,  each  load 
containing  12  barrels  of  2^  bushels  each,  at  $.50  per  bushel, 
for  a  number  of  pieces  of  cloth,  eaqji  containing  12  yards, 
worth  $2.75  per  yard.     How  many  pieces  did  he  receive  ? 

275.  IIow  many  feet  of  boards  will  it  require  to  inclose  a 
barn  40  ft.  6  in.  long,  30  ft.  10  in.  wide,  18  ft.  4  in.  high,  and 
each  side  of  the  roof  16  ft.,  allowing  385  ft.  3  in.  for  the  gables  ] 

276.  What  is  the  value  of  .05751953125  Cong. 

277.  A  degree  of  longitude,  in  the  latitude  of  Boston, 
measures  44.1  geographic  miles.  How  many  more  statute 
miles  in  10°  of  longitude  at  the  equator  than  in  the  latitude 
of  Boston  1 

278.  Rhode  Island  in  1862  expended  $168365  in  educating 
27750  children.     What  was  the  average  expense  per  child '? 

279.  In  the  same  year  Ohio  spent  $2834066  for  the  cduca- 


ARITHMETICAL   EXAMPLES.  107 

tion  of  717726  children.     How  much  more  did  Pdiode  Island 
expend  per  child  than  Ohio  ? 

280.  Massachusetts,  during  the  same  period,  paid  out 
$1612824  for  the  instruction  of  220010  children.  How  much 
did  the  average  expense  per  child  in  Massachusetts  lack  of 
being  twice  the  expense  incurred  by  Ohio  for  each  child  1 

281.  How  many  inches  higher  is  a  horse  that  measures 
16^  hands  than  one  that  stands  14|  hands  high  ? 

282.  A  person,  dying,  left  in  cash  $6250,  and  4  houses, 
valued  at  $3-456.785  each;  his  hidebtedness  was  ^2261.60, 
and  he  left  directions  that  $100  should  be  expended  for  a 
monument;  the  residue  was  to  be  divided  among  his  4 
sons,  so  that  each  should  receive  J  as  much  as  his  next  older 
brother.     Required  the  share  of  each. 

283.  If  there  are  31181  verses  in  the  Bible,  and  a  person 
reads  88  verses  on  Sunday,  how  many  must  he  read  each 
week-day  to  complete  it  in  a  common  year  ? 

284.  A  tract  of  land  measuring  4059  A.  2  R.  16  P.  was 
divided  among  a  regiment  of  men,  consisting  of  one  colonel, 
1  major,  6  captains,  8  lieutenants,  24  sergeants,  and  220 
privates,  so  that  a  private  had  one  share,  a  sergeant  twice  as 
much,  a  lieutenant  6  shares,  a  captain  8,  the  major  14,  and 
the  colonel  20  shares.     Required  the  share  of  each  1 

285.  From  the  sum  of  |  lb.  2/^  oz.  15 J  pwt,  take  the  dif- 
ference between  |  oz.  and  |  pwt, 

286.  The  earnings  of  the  Toledo  and  Wabash  P.ailroad  Com- 
pany in  1862  were  $1374517,  which  was  4  J  ^^  the  earnings 
in  1863;  the  expenses  each  year  were  $47721  more  than 
half  the  earnings  in  1863.  How  much  more  were  the  net 
earnings  of  1863  than  of  18()2  ? 

287.  What  is  the  least  nuniber,  which,  being  divided  by 
3,  5,  7,  9,  and  10,  leaves  a  remainder  of  one? 

288.  What  part  of  a  hogshead  of  wine  is  3  gal.  1  qt.  2  fg 
gills? 


108  ARITHMETICAL    EXAMPLES. 

289.  A  speculator  in  New  York  bought  1000  bushels  of 
grain  at  ll.lO  per  bushel,  and  shipped  the  same  to  England, 
paying  $125  transportation;  he  sold  the  grain  at  ^1.40  per 
Imperial  bushel.     What  was  his  gain  1 

290.  If  the  diameter  of  the  sun  be  884000  miles,  and  that 
of  the  earth  8000  miles,  how  many  bodies  of  the  size  of  the 
earth,  placed  in  a  line,  would  reach  across  the  sun's  diameter  1 

291.  Reduce  6  leagues,  2  mi.  3  fur.  17  rd.  4  ft.  1^  in.  to 
statute  miles. 

292.  The  Austrian  empire  contains  7889925  Germans, 
15027646  Slavi,  5632689  Roumanians,  4947134  Magyars, 
and  of  other  races  a  number  making  the  entire  population 
34714326.    How  many  belong  to  nationalities  not  mentioned  1 

293.  Paid  in  London  £195^  for  12  bales  of  cloth.  How 
many  bales  should  be  received  for  £536 j^^  ? 

294.  A  farmer  sold  8  loads  of  potatoes,  averaging  27  bu. 
3  pk.  5  qt.  each,  for  $.45  a  bushel.  How  much  did  he  re- 
ceive ? 

295.  Divide  $897.43  among  A,  B  and  C,  so  that  B  may 
have  $93.40  less  than  A,  and  $69.18  more  than  C. 

296.  If  the  population  of  the  world  be  as  follows,  viz. : 
Asia,  630700000;  Europe,  265494300;  Africa,  61700000;^ 
America,  57600000 ;  Oceanica,  23400000 ;  and  the  average 
length  of  life  be  33 y%  years,  what  is  the  average  number  of 
deaths  each  day  ?  , 

297.  How  many  more  bushels  will  a  cubical  box  contain, 
whose  sides  measure  8  ft.,  than  one  that  is  10  ft.  long,  8  ft. 
wide,  and  6  ft.  deep  ? 

298.  How  many  seconds  in  40  tropical  years,  340  da.  22  h. 
37  min.  45  sec.  ? 

299.  A  surveyor,  measuring  a  piece  of  land  in  the  form  of 
a  rectangle,  found  one  side  to  be  55  ch.  50  1.,  and  the  other, 
63  ch.  24  1.     How  many  acres  did  it  contain  ? 

300.  In  Ohio  there  are  997  miles  of  canals,  the  aggregate 


ARITHMETICAL    EXAMPLES.  109 

receipts  from  which  for  a  period  of  15  years,  were  88521630.- 
42.     Required  the  average  annual  receipts  per  mile. 

SOL  A  block  of  granite  containing  126  ft.  10'  11",  is  2  ft. 
6'  wide,  and  3  ft.  7'  thick,  what  is  its  length  ? 

302.  If  a  young  man,  by  early  rising,  can  save  2A  hours 
each  day  for  study  and  improvement,  how  many  years  of 
study  can  be  gained  in  25  years,  allowing  365  days  in  a  year, 
and  12  hours  in  a  day  1 

303.  Alexander  Wilson  estimated  that  a  flock  of  pigeons 
which  was  6  hours  in  passing,  was  one  mile  in  breadth  and 
flew  at  the  rate  of  40  miles  per  hour ;  allowing  3  pigeons  to 
a  square  yard,  what  was  the  estimated  number  of  pigeons  in 
the  flock  ? 

304.  How  much  cloth  at  84.00  per  yd.,  must  be  given  for 
9  tons,  8  cwt.  3  qr.  12A  lb.  of  sugar  at  89.50  per  cwt.  1 

305.  If  22|  cords  of  wood  last  as  long  as  I5/3  tons  of  coal, 
how  many  cords  of  wood  will  last  as  long  as  11  ^fg  tons  of  coal  1 

306.  A  fruit  grower  put  178  bu.  1  pk.  6  qt.  1  pt.  of  cherries 
into  casks,  each  containing  2  bu.  3  pk.  6  qt.,  and  sold  them 
for  8315.90.     How  much  did  he  receive  per  cask  ? 

307.  The  Post  Office  receipts  in  New  York  for  the  year 
ending  June  30,  1861,  were  as  follows :  Letter  postage, 
1191879.63;  newspaper  postage,  880153.42;  registered  let- 
ters, 82679.10  ;  stamps  sold,  81460955.89  ;  the  expenditures 
for  the  same  period  were  8344757.04  for  salaries  of  post- 
masters ;  8328661.44,  incidental  expenses  ;  $444166.75,  trans- 
portation of  mails.  What  was  the  net  income  to  the  Post 
Office  Department  for  that  year  from  the  State  ? 

308.  If  a  grocer  use  scales  that  weigh  15  oz.  4  dr.  for  a 
pound,  how  much  does  he  cheat  in  selling  855.04  worth  of 
sugar  1 

309.  Three  men  cut  15^  cords  of  wood  in  2|  days,  for 
which  they  received  811.62^.  What  were  the  average  daily 
wages  of  each  man  1 


110  ARITHMETICAL    EXAMPLES. 

310.  A  merchcant  bought  150  gallons  of  molasses  at  $.60  a 
gallon,  and  intended  to  have  it  sold  at  8.75  a  gallon,  but  his 
clerk,  by  mistake,  sold  half  of  it  by  beer  measure  at  |.15  a 
quart ;  discovering  the  blunder  he  directed  him  to  sell  the  re- 
mainder at  i,%18  a  quart,  wine  measure.  How  much  more 
than  the  cost  did  he  receive  for  the  molasses  ? 

311.  A  meteorological  observer,  in  Cayuga  County,  New 
York,  registered  the  total  fall  of  rain,  in  1861,  of  34.86  in.; 
of  snow,  40j495  in.,  and  3.5  in.  of  snow  made  one  inch  of 
water.  How  many  hogsheads  of  water  fell,  during  the  year, 
in  the  town  of  Genoa,  which  is  10  miles  square? 

312.  The  whole  length  of  railroads  in  the  United  States 
Jan.  1,  1852,  was  10900  miles;  ten  years  after,  the  mnnber 
of  miles  open  for  traffic  was  23  less  than  ^J^j  times  this  num- 
ber of  miles;  the  total  cost  of  the  roads  and  equipments,  at 
the  last  period  mentioned,  was  $1192400424.  What  was  the 
average  cost  per  mile  in  1862? 

ol3.  How  many  pipes  of  Port  are  equal  to  23  of  Sherry? 

314.  If  there  are  371.25  grains  of  pure  silver  in  one  dollar, 
how  many  silver  dollars  are  equivalent  in  value  to  5.6  lb.  of 
English  standard  gold  ?  -r 

315.  What  cost  4  bundles,  1  ream,  6  quires, '12  sheets  of 
paper  at  $45.72  per  bundle? 

316.  The  Austrian  army,  in  1863,  was  composed  of  160316 
active  infantry ;  424000  reserve ;  the  active  cavalry  was  | 
the  active  infantry,  less  235;  the  reserve  cavalry,  2490  less 
than  I  the  reserve  infantry ;  all  other  active  troops,  5674 
more  than  the  active  cavalry ;  and  all  other  reserve  troops 
were  169  less  than  all  the  cavalry;  the  population  being 
34714326,  what  proportion  of  the  people  were  soldiers? 

317.  Gunpowder  made  according  to  the  government  re- 
ceipt, is  a  compound  of  |  nitre,  and  equal  parts  of  sulphur 
and  charcoal.     How  much  of  each  in  1  ton  of  powder? 

318.  How  many  cubic  quarter  inches  in  a  slab  of  marble 
2  yd.  long,  1  ft.  6  in.  wide,  3  in.  thick  ? 


ARITHMETICAL    EXAMPLES.  Ill 

319.  A  ship  captain,  sailing  from  London  to  New  York, 
found,  on  taking  an  observation,  that  the  sun  at  noon  was  3  h. 
25  min.  40  sec.  hiter  than  the  London  time,  as  shown  by  his 
chronometer.     How  many  degrees  west  had  he  sailed  ? 

820.  In  1855  the  U.  S.  Government  sold  15729524  acres 
of  public  lands,  for  $11246009.60.  How  much  did  John 
Smith  paj  fcr  a  quarter  section,  at  the  average  price  per  acre  ? 

321.  A  farmer  planted  a  field,  30  rods  long  and  20  rods 
wide,  with  corn ;  the  hills  were  in  squares,  3  feet  apart,  and 
the  outside  rows  1  ft.  6  in.  from  the  fence ;  allowing  each  hill 
to  produce  5  ears,  and  8  ears  to  make  a  quart,  how  much  was 
the  corn  raised  on  the  field  worth  at  $.80  a  bushel  1 

322.  The  five  diflTerent  races  number  as  follows  :  American, 
11000000;  Malay,  twice  as  many  +  1500000;  Ethiopian, 
30000000  more  than  the  ]\Ialays ;  Caucassian,  ^  the  whole 
population  of  the  earth — 19400000 ;  and  the  Mongolians, 
450800000.  How  many  more  Caucassians  than  Mongolians, 
and  what  is  the  total  population  of  the  earth  ? 

323.  If  the  longitude  of  Boston  is  70°  4'  AVest,  what  will 
be  the  time  in  that  place  when  it  is  3  h.  S5  min.  A.  M.  in 
London  ? 

324.  Albert  Tucker,  owning  80  acres  of  land,  cultivated  H 
acres  potatoes,  3|  corn,  2j  rye,  1|  oats,  J  carrots,  J  turnips, 
from  which  he  harvested  160  bushels  potatoes,  4SJ  corn,  28 
rye,  56^  oats,  650  carrots,  and  720  turnips  per  acre,  respec- 
tively. He  cut  1|  tons  hay  on  each  of  12|  acres,  and  upon 
the  remainder  he  pastured  30  sheep,  5  cows,  2  horses  and  8 
steers,  for  24  weeks.  He  sold  his  potatoes,  corn,  rye,  oats, 
carrots  and  turnips  at  $.75,  $1.12i,  $1.25,  $.40,  $.25  and  $.15 
per  bushel,  respectively  ;  he  sold  his  hay  at  $16  per  ton,  and 
received  3,  20,  45  and  15  cents  each  per  week,  respectively, 
for  pasturing  the  sheep,  cows,  horses  and  steers.  "What  were 
the  net  profits  of  the  farm,  supposing  he  paid  $25  taxes,  and 
$30,  $28,  $16,  $16,  $40,  $32  and  $5  per  acre,  respectively, 
for  cultivating  and  harvesting  the  potatoes,  corn,  rye,  oats, 
carrots,  turnips  and  hay  1 


CHAPTEE  Y. 

1.  My  salary  is  1800  a  year.  I  pay  o5%  of  it  for  board, 
115^  for  clothing,  12^  for  books,  and  7%  for  incidentals. 
How  much  are  my  yearly  expenses  ? 

2.  If  13^-  bushels  of  wheat  make  3  barrels  of  flour,  how 
many  bushels  of  wheat  will  be  required  to  make  40  barrels 
of  flour  1 

3.  A  farmer  raised  20^  more  of  wool  this  year  than  last ; 
the  amount  raised  during  the  two  years  was  1320  lbs.  What 
amount  of  wool  was  raised  each  year  ? 

4.  A  horse  which  cosfc  me  ill 35  I  sold  for  $150,  on  9 
months'  credit.     How  much  did  I  gain,  money  being  worth  6^  ? 

5.  The  debt  created  by  the  U.  S.  Government  from  March 
7,  1861,  to  July  1,  18(52,  was  $451456866;  $125090  more 
than  j';j  of  this  pertained  to  civil  affairs ;  the  remainder  was 
caused  by  the  war.  How  much  did  the  rebellion  expenses 
average  per  day  1 

6.  I  purchased  6000  bushels  of  wheat  in  Chicago  at  $1.37^, 
and  shipped  the  same  to  my  agent  in  Albany,  who  sold  it  at 
$1.62.1.  How  much  did  I  make,  after  paying  $543  for  ex- 
penses and  a  commission  of  21^? 

7.  A  man  sleeps  7. J-  hours  each  day.  What  per  cent,  of 
his  time  does  he  sleep? 

8.  The  amount  of  money  deposited  in  the  savings  banks 
of  New  York,  in  1863,  w^as  $54557500 ;  the  amount  with- 
drawn from  the  same  during  the  year  was  $11347960. 
What  per  cent,  of  the  amount  deposited  was  withdrawn,  and 
how  much  was  the  annual  interest  at  5^  on  the  money  re- 
maining 1 

9.  If  24  men,  in  9  days  of  12  hours  each,  build  a  wall  200 


ARITHMETICAL    EXAMPLES 


113 


feet  long,  6  feet  high  and  2  feet  thick,  how  many  men,  in  72 
days  of  10  hours  each,  can  build  a  wall  950  feet  long,  8  feet 
high  and  5  feet  thick  1 

10.  A  man  drew  30^  of  his  bank  deposits,  and  expended 
25^  of  the  money  thus  drawn  to  purchase  a  horse,  worth 
1^97.50.     How  much  money  had  he  in  bank  ? 

11.  A  grocer  bought  2  T.  14^  cwt  of  cheese  at  S240  per 
ton,  and  retailed  the  same  at  IG  cents  per  pound.  What  per 
cent,  was  his  profit  1 

12.  The  capital  of  an  insurance  company  is  8250000;  its 
receipts  for  one  year  are  858760 ;  its  losses  and  expenses  are 
840010.     What  rate  of  dividend  can  it  declare  1 

13.  If  360  bushels  of  oats  will  last  12  horses  15  days,  how 
long  will  636  bushels  last  18  horses  ] 

14.  I  own  25  shares  of  850  each  in  the  ^tna  Insurance 
Co.,  which  has  declared  a  semi-annual  dividend  of  3^^. 
How  much  do  I  receive  ? 

15.  If  4  J  bushels  of  potatoes  arc  sold  for  81.50,  how  much 
r.rc  27.25  bushels  worth  ? 

16.  A  railroad  jobber  contracted  to  build  20  mi.  5  fur.  25 
rd.  of  railroad  for  825000  per  mile  ;  after  finishing  the  work, 
he  found  the  actual  cost  was  875  per  rod.  How  much  did  he 
clear  by  the  job,  and  what  was  the  rate  of  his  profit  ? 

17.  A  man,  Avishing  to  sell  a  horse,  asked  25^  more  than 
it  cost;  he  finally  sold  it  for  15^  less  than  his  asking  price, 
and  gained  87.50.  How  much  did  the  horse  cost  him,  and 
what  was  his  asking  price  1 

18.  Required  the  average  maturity  of  the  following  ac- 
count : 

A.  Z.  Armour. 

Dr-  Cr. 


1859.     1 

1 

1        1S59. 

== 

Feb.   12 

To  Mdsa 

85 

75 

1  March  15 

By  bal.  old  acc't. 

97 

F6 

"     25 

36 

i'4 

!  April    17 

"  cash 

.'56 

00 

April  16 

"      *' 

174 

m 

1   M;iy      £5 

25 

00 

May    20  1 

"       " 

1     94 

78 

1  June       S 

"   sundries 

94 

75 

114  ARITHMETICAL    EXAMPLES. 

19.  The  expenses  of  a  school  for  one  year  were  ^2000  for 
salary  of  teachers,  $105.50  for  fuel,  $56.25  for  incidentals; 
the  public  money  was  $750.75,  and  the  remainder  was  paid 
by  a  rate  bill.  If  the  aggregate  attendance  was  35275  days, 
how  much  must  John  Spencer  pay,  who  sent  3  pupils  175 
days  each  ? 

20.  Sold  I  of  a  hhd.  of  molasses  for  what  the  whole  cost 
me.     What  was  my  gain  per  cent.  ?  -• 

21.  When  does  the  amount  of  the  following  bill  become 
due,  per  average  ? 

George  Barbour, 

1864.  To  J.  B.  Hale  &  Co.,  Dr. 

Jan.      20     .     To    100  yd.  Broadcloth  .     ®     S3.25 

25     .      "  2500    "    Sheeting    .         .     ©         .12 

March  20     .       "    3000    "    Merrimac  Prints     ©         .18 

April      1     .      "      300    "    French  Silk        .     ©       1.75 

22.  If  a  man,  by  laboring  12  hours  each  day,  can  perform 
a  piece  of  work  in  3  weeks,  by  laboring  6  days  in  a  week, 
how  long  would  it  take  him  to  do  the  same,  if  lie  labor  10 
hours  each  day  % 

23.  Bought  4  hhd.  of  sugar,  each  containing  1825  lbs.,  at 
6|  cents  per  pound,  and  paid  $31,975  for  freight,  storage  and 
cartage.  Allowing  5^  for  leakage  and  waste,  for  how  much 
per  pound  must  I  sell  the  remainder  to  gain  25^  % 

24.  Bought  a  house  for  $4500,  and  paid  $500  cash;  the  bal- 
ance is  to  be  paid  in  8  equal  annual  installments.  What  is 
the  mean  time  for  paying  the  balance  % 

25.  What  is  the  difference  between  the  interest  and  dis- 
count of  $337.50  for  1  yr.  4  mo.,  at  6^^? 

26.  Sold  a  horse  at  33^^  gain,  and  with  the  money  bought 
another  horse,  which  I  sold  for  $120,  and  lost  25^.  Did  I 
gain  or  lose  by  my  trading  ?  and  how  much  ? 

27.  An  insurance  agent,  whose  commission  was  10;^  on  all 


ARITHMETICAL   EXAMPLES. 


115 


sums  received  for  the  company,  cleared  $1524.45  in  one  year. 
What  were  the  company's  net  receipts  from  the  agent  ? 


^ 


28.  In  1862  the  cavalry  in  the  French  army  were  'i9r^-^yo 
of  the  infantry  ;  the  artillery  were  G6%  of  the  cavalry  ;  the 
engineers  were  22 -S_^  of  the  artillery  ;  and  the  gens-d'armes 
.39  of  the  artillery.  If  the  engineer  corps  numbered  15000 
men,  what  was  the  strength  of  each  of  the  other  arms  ? 

29.  The  Financial  Committee  of  a  graded  school  invested 
833901.  in  U.  S.  7-j^  Treasury  Notes,  which  were  at  a  prem- 
ium of  4|^,  as  a  fund  for  the  support  of  the  school ;  the  sal- 
aries of  teachers  amounted  to  $1975,  and  8227.04  was  paid 
for  incidentals.     "What  sum  was  annually  left  unexpended  1 

30.  If  12  boarders  eat  825  worth  of  bread  in  2  mo.,  when 
flour  is  89.50  per  barrel,  in  how  many  months  will  15  board- 
ers eat  860  worth  of  bread,  when  flour  is  812  per  barrel  ? 

31.  A  shipment  of  wheat  was  insured  at  2?^,  to  cover  |  of 
its  value;  the  premium  paid  was  44.07;  the  wheat  being 
worth  8.80  per  bushel,  how  many  bushels  were  shipped  ? 

32.  Which  is  the  more  profitable  to  buy  7's  at  105;;^,  or  5's 
at  80^  1 

33.  The  cash  capital  of  the  West  Roxbury  Horse  Railroad 
Company  is  $40400;  the  net  receipts  for  one  year  were 
83312.  If  2  0?  ^^  ^^^  ^^^  receipts  be  reserved  in  favor  of  the 
Company,  how  large  a  dividend  may  be  declared  1 

34.  A,  who  is  worth  86845,  is  taxed  $55.14;  what  is  B 
worth,  who  is  taxed  $256.18  '? 

35.  J.  Burns  in  account  with  Tyler  &  Co. 

Dr.  Cr. 


1860. 

-'  1 

—  1 

1      1S60. 

— 

Feb.      25 

To  Mdse.  on  3  mo.     SCO 

75 

March  1 

By  Cash  on  acct.         250 

00 

March  20 

"      "  3    "        240 

56 

i  April  20 

"  Accept,  at  30  da.  1  300 

00 

April    26 

24 

1  June  12 

"    Sundries,               1875 

00 

June     24 

"      "  2    "        235 

25  ! 

1      "      27 

"    Cash  on  acct.        1  400 

00 

Required  the  cash  value  of  the  above  account,  July  1,  1860, 
interest  at  6^. 


116  ARITHMETICAL    EXAMPLES. 

36.  The  loans  and  discounts  of  all  the  banks  of  Philadel- 
phia amounted  to  $29705200,  Oct.  19,  1861  ;  the  specie  in 
vaults  was  $6375750;  the  deposits  $21100085;  and  the 
capital  stock  paid  in,  $11811500.  On  the  first  of  Jan.,  1863, 
the  loans  and  discounts  had  increased  26|  per  cent. ;  the 
specie  had  diminished  29  J  per  cent. ;  the  deposits  were  ^^3 
more ;  and  the  capital  stock  paid  in,  g  of  one  per  cent,  less 
than  in  Oct.  1861  :  loans,  discounts,  and  specie  being  re- 
sources ;  deposits  and  capital  stock  being  liabilities,  how  much 
were  the  resources  in  excess  of  the  liabilities,  Jan.  1,  1863? 

37.  A  stack  of  hay  will  keep  24  cows  or  IS  horses  one 
week.     How  many  days  v/ill  it  keep  5  cows  and  5  horses  ? 

38.  A  merchant  pays  $10050  for  a  stock  of  goods;  he  sells 
them  at  an  advance  of  33  J  ^ ;  the  expenses  connected  with  the 
business  are  $1750.     How  much  does  he  gain? 

39.  The  value  of  real  estate  and  personal  property  in  Ken- 
tucky in  1850  was  $301628456;  in  1860  it  was  $666043112. 
What  was  the  increase  per  cent,  in  10  years'? 

40.  The  value  of  real  estate  and  personal  property  in  Illi- 
nois in  1850  was  $1562655006 ;  in  1860,  $871860282.  What 
was  the  increase  per  cent,  in  10  years  1  How  many  times 
as  great  was  the  increase  of  property  in  Illinois  than  in  Ken- 
tucky ? 


41.  $1200-i-Vo-  Boston,  Feb.  1,  1863. 

Six  months  after  date  I  promise  to  pay  Knowles, 
Leland,  &  Co.,  or  order,  twelve  hundred  and  {'q%  dollars,  with 
interest,  for  value  received.  S.  M.  Smith. 

Indorsed  as  follows:  April  16,  1863,  $215.77;  Aug.  1, 
1863,  $317.50;  Dec.  16,  1863,  $315.75.  How  much  was 
due  April  1,  18G4? 

42.  A  farmer  bought  100  oxen,  cows,  and  slieep  for  $1160; 
there  were  6  times  as  many  cows  as  oxen,  and  3  times  as 
many  sheep  as  cows ;    the  oxen  cost  twice  as  much  per  head, 


ARITHMETICAL   EXAMPLES.  117 

and  the  sheep  i  as  much,  as  the  cows.     How  many  oxen, 
cows,  and  sheep  were  bought  ?  and  at  what  price  1 

43.  What  per  cent,  is  gained  by  buying  oil  at  80  cents  a 
gallon,  and  selling  it  at  12  cents  a  pint  ? 

44.  A  man  bought  a  farm  of  160  acres  at  832  per  acre; 
he  paid  $200  for  fencing,  8150  for  repair  of  buildings,  and 
$18  for  improving  the  grounds;  at  w^hat  price  per  acre  must 
it  be  sold  to  gain  25^  on  the  entire  cost  1 

45.  The  taxable  property  of  a  School  District  is  8756000 ; 
a  Union  School-house  is  to  be  built,  worth  824956.16;  the 
number  of  taxable  polls  is  520,  each  of  which  is  assessed 
81.50.  Allowing  S%  for  collecting,  what  will  be  the  tax 
upon  81.00'?  and  how  much  will  be  the  tax  of  S.  P.  Norton, 
who  pays  for  2  polls,  and  is  worth  815420  ? 

46.  If  6  men  in  8  days,  working  10  hours  each  day,  can 
cut  40  acres  of  grass,  how  many  men  in  12  days,  by  working 
8  hours  a  day,  can  cut  96  acres  1 

47.  If  the  use  of  8250  for  1  yr.  8  mo.  is  worth  830,  how 
much  is  the  use  of  8425.50  for  3  yr.  7  mo.  25  da.  worth  ? 

48.  What  must  be  the  face  of  a  note  at  60  days,  the  pro- 
ceeds of  which,  w'hen  discounted  at  Bank  at  6^,  are  8100? 

49.  A  western  grain-dealer  bought  wheat  as  follows,  viz. : 
400  bushels  of  red  wheat  at  81.40;  800  bushels  of  white 
wheat  at  81.62A  ;  and  300  bushels  of  spring  wheat  at  81.20: 
he  shipped  the  whole  to  his  correspondent  in  Albany,  who 
sold  the  first  kind  at  an  advance  of  15^,  the  second  at  an  ad- 
vance of  20^,  and  the  third  at  81.15  per  bushel :  deducting 
from  the  gross  proceeds,  his  commission  at  3^,  8108.23  for 
expenses,  he  remitted  to  the  consignor  the  net  proceeds. 
What  was  the  rate  of  the  grain-dealer's  gain  1 

50.  If  8400  gain  816  in  8  months,  what  is  the  rate  of  in- 
terest '? 

51.  A  town  levies  a  tax  for  building  a  bridge,  which  costs 


118  ARITHMETICAL    EXAMPLES. 

$?2520 ;   allowing  4^  for  collecting,  for  what  sum  must  the 
tax  be  levied  ? 

52.  A  merchant  tailor  bought  4  pieces  of  cloth,  each  con- 
taining 30  yd.  3.75  qr.,  at  ^2.00  per  yd. ;  he  sold  ^  of  it  at 
12.20  per  yard,  and  made  up  the  remainder  into  suits,  each 
containing  7  yd.  2  qr.,  which  he  sold  for  $18.50  each.  How 
much  did  he  gain  1 

53.  What  sum  must  I  invest  in  United  States  6's,  selling 
at  2-1^  premium,  to  secure  an  annual  income  of  $840  1 

54.  What  is  the  rate  of  income  upon  money  invested  in 
6  per  cent,  bonds,  purchased  at  a  discount  of  10  per  cent.  1 

55.  If  it  require  192  reams  of  paper  to  print  2400  copies 
of  an  8vo  book,  containing  440  pages,  how  many  reams  will 
be  required  to  print  6000  copies  of  a  16mo  book,  containing 
220  pages  1 

56.  Goodman  and  Barbour  bought  bills  of  goods  of  Mellen, 
Claflin,  and  Co.,  New  York,  as  follows,  viz. :  Jan.  1,  1863, 
$750;  June  1,  1863,  $1250;  Sept.  16,  $2525;  Dec.  31, 
1863,  $895.65  :  they  bought  on  time,  paying  legal  interest. 
What  was  their  whole  indebtedness,  May  1,  1864? 

57.  What  must  I  pay  for  U.  S.  6  per  cents,  that  the  invest- 
ment may  yield  8  per  cent.  1 

58.  A  man,  dying,  left  $3565  to  be  placed  at  interest  for 
his  son,  who  was  16  yr.  5  mo.  15  da.  old;  how  much  will  he 
receive  when  he  is  21  years  old,  allowing  7%  interest "? 

59.  The  population  of  New  York  city,  in  1860,  was  805650 ; 
it  was  estimated  to  have  increased  20  per  cent.  Jan.  1,  1864. 
Suppose  at  this  last  date  the  whole  population  were  drawn 
up  in  single  file,  each  person  occupying  a  space  of  2A  ft.,  and 
the  whole  line  should  begin  to  march  at  the  rate  of  2A  miles 
per  hour,  what  would  be  the  length  of  the  line,  and  how  long 
would  the  procession  be  in  passing  any  given  point  1 

60.  A  house  being  rented  for  $12  a  month  pays  7|  per 
cent,  interest,  what  is  the  value  of  the  house  ? 


ARITHMETICAL    EXAMPLES  119 

61.  Bought  5000  bushels  of  wheat  on  0  months'  credit,  at 
81.37^  ;  I  immediately  sold  it  at  $1.85  cash,  and  put  out  the 
money  at  Q% ;  at  the  end  of  0  months  I  paid  for  the  wheat. 
Did  I  gain  or  lose  by  the  transaction,  and  how  much  ? 

62.  Thomas  Baker  bought  a  farm  for  $20000  cash,  or 
810000  payable  in  6  months,  and  $12000  in  1  yr.  6  mo. ;  he 
chose  the  latter  mode  of  payment.  Money  being  worth  7^ 
did  he  gain  or  lose,  and  how  much  1 

63.  The  earnings  of  the  Chicago  and  Northwestern  R.  R. 
for  the  week  ending  Jan.  14,  1864,  were  $6926.12  more  than 
for  the  same  period  in  1863 ;  the  earnings  for  the  week  men- 
tioned, in  1864,  being  an  increase  of  48^  over  the  earnings 
of  the  corresponding  week  of  the  previous  year,  what  were 
the  earnings  for  the  week  in  1864? 

64.  A's  money  is  50^  more  than  B's.  How  many  per 
cent,  less  is  B's  than  A's  ? 

65.  Bought  450  barrels  of  flour  at  $8.50,  which  I  paid  for 
in  iron  at  3  cts.  per  pound ;  the  purchaser  of  the  iron  after- 
wards sold  J  of  it  to  a  scythe  manufacturer.  What  quantity 
did  he  sell  1 

66.  What  is  the  diiference  between  the  simple  and  com- 
pound interest  of  $700  in  3  years  at  5  per  cent,  per  an- 
num 1 

67.  Reduce  9  sq.  rd.  9  sq.  yd.  7  sq.  ft.  120  sq,  m.  to  the 
decimal  of  J-  of  |  of  f  of  35  A.  2R. 

68.  A  man  dying  left  33|^  of  his  property  to  his  wife; 
50^  of  the  remainder  to  his  son  ;  75^  cent  of  the  .residue  to 
daughter,  and  the  balance,  $120,  to  a  faithful  servant.  How 
much  did  each  receive  1 

69.  A  house  that  cost  $3125,  was  rented  for  $328.12^. 
^Yhat  per  cent,  did  it  i^ay  on  the  investment  ? 

70.  A  grocer  bought  60  gallons  of  milk  by  beer  measure 
at  4  cents  a  quart,  and  sold  it  by  w^ine  measure  at  5  cents  a 
quart.     How  much  was  his  gain  ? 


120  ARITHMETICAL    EXAMPLES. 

71.  If  I  borrow  $1000  in  Mass.  and  lend  it  in  New  York, 
how  much  do  I  gain  in  1  yr.  3  mo.  20  da.  ? 

72.  The  total  population  of  America  is  70415000,  Zd%  of 
which  are  Protestants ;  the  total  population  of  Europe  is 
2S2823000,  23^  of  which  are  Protestants.  How  many  more 
Protestants  in  Europe  than  in  America  1 

73.  If  300  sheep  require  150  A.  3  Pt.  36  P.  of  pasture,  how 
many  acres  will  450  sheep  require? 

74.  I  sent  $12300  to  my  agent  in  New  York,  with  which 
to  purchase  flour  at  $10  per  barrel,  after  deducting  his  com- 
mission of  2^5^.     How  many  barrels  of  flour  did  I  receive? 

75.  A  manufacturer  eflected  an  insurance  upon  his  factory 
and  machinery,  valued  at  $20000,  paying  an  annual  premium 
of  2^ ;  in  the  second  year  the  establishment  was  damaged  by 
fire  to  the  amount  of  $1560.  How  much  did  he  save  by  the 
insurance  ? 

76.  Average  the  following  account : 

John  Lyman. 

Dr.  Cr. 


I860.     1 

1 

1     1860. 

1 

—— 

June  12  1  To  Mdse. 

530 

GO 

1  June  24 

By  draft  at  30  da. 

1  480 

00 

Sept.  12      "      " 

4-28 

00 

i  Aug.    20 

"   cash, 

280 

00 

Oct,    23      "      " 

440 

0) 

1  Oct.      8 

"      " 

140 

03 

77.  Three  persons  purchased  a  block  of  tenements  for 
$350000,  of  which  A  paid  $150000  ;  B,  $80000 ;  C,  $120000  ; 
the  net  proceeds  of  the  rent  were  $21000.  How  much  should 
each  receive  1 

78.  How  much  gold,  silver  and  copper  in  an  eagle,  its 
weight  being  10  pwts.  18  gr.  ? 

79.  A  capitalist  invested  §  of  his  money  in  P.  P.  stock, 
which  depreciated  6|^ ;  the  remainder  he  invested  in  real 
estate,  which  advanced  15^^^,  and  thereby  he  gained  $1500. 
How  much  did  he  gain  in  both  investments? 

80.  Boise,  Smith  &  Co.  failed  in  business ;  their  indebted- 
ness was  $75000  ;  their  assets  were,  Cash,  $3000;  Mdse.,  $15- 
500 ;  Store,  $28000 ;  Bills  Receivable,  $5500 ;  the  expenses  of 


ARITHMETICAL    EXAMPLES.  121 

settling  were  4:%  of  the  amount  distributed  to  the  creditors. 
What  per  cent,  of  their  indebtedness  can  they  pay  1 

81.  If  3  yd.  3  qr.  1  na.  cost  812.20,  how  much  will  18  yd. 
2  qr.  1  na.  of  the  same  cloth  cost  ? 

82.  Bought  a  hogshead  of  molasses  for  a  certain  sum,  but 
IG  gallons  having  leaked  out,  the  remainder  was  sold  for 
C-^l.ST^  per  gallon,  at  a  loss  of  G^  on  the  cost.  Ilovr  much 
was  the  cost  ? 

83.  A  merchant  bo't  400  yds.  broadcloth  ©  83.00 ;  he  sold 
A  60  yds.  @.  83.50 ;  B,  125  yds.  ®  83.40  ;  C,  75  yds.  ©  83.20 ; 
and  the  balance  to  D  @  82.95.  What  per  cent,  profit  did  he 
make  on  the  whole  ? 

84.  Jan.  1,  18G3,  Rhode  Island  had  sent  1462G  men  to  the 
war;  Connecticut  1033  less  than  twice  as  many;  Maii:;e, 
4886  more  than  Connecticut ;  New  Hampshire  and  Vermont 
together,  36S0  more  than  Maine;  and  Massachusetts,  1189 
more  than  Maine,  New  Hampshire  and  Vermont.  How 
many  men  had  the  New  England  States  sent  to  the  army  1 

85.  An  agent  for  a  Hartford  nurseryman  sells  5000  apple 
trees  at  824  per  hundred';  3000  pear  trees  at  840  per  hun- 
dred; 2000  peach  trees  at  818  per  hundred;  1500  cherry 
trees  at  845  per  hundred ;  500  plum  trees  at  845  per  hun- 
dred, and  1000  ornamental  trees  at  850  per  hundred.  What 
is  his  commission,  at  25^,  and  how  much  should  he  return  to 
his  employer,  as  the  net  proceeds  after  deducting  8300  for 
expenses  ? 

86.  How  much  is  gained  by  investing  85250  in  government 
bonds  at  105^,  brokerage  1|^,  and  selling  the  same  at  116^, 
brokerage  1|^? 

87.  A  man  traveled  19f  miles  the  first  day,  22 A|  miles  the 
second  day,  and  19  mi.  1  fur.  20  rds.  15|  feet  the  third  day. 
How  fir  did  he  travel  in  the  three  days  1 

88.  A  broker  charges  me  ItJ^  for  purchasing  some  uncur- 
rent  bank  bills  at  25^  discount;  of  these  bills,  three  of  810 


122  ARITHMETICAIr  EXAMPLES. 

each,  and  one  of  |50  became  Avorthless ;  I  dispose  of  the  re- 
mainder at  par,  and  thus  make  $520.  What  was  the  amount 
of  bills  purchased  ? 

89.  I  bought  2345  bushels  of  wheat  at  $1.20,  and  imme- 
diately sold  it  at  $1.30,  on  a  note  of  6  months,  which  I  got 
discounted  at  bank  at  7  per  cent.     How  much  did  I  gain  ? 

90.  I  sent  $9020  to  my  agent  in  Chicago,  who  purchased 
grain  at  an  average  price  of  $1.10  per  bushel,  and  charged 
2A^  commission.     How  many  bushels  did  he  buy  1 

91.  On  the  first  of  Jan.,  1862,  there  were  10869  miles  of 
railroad  in  operation  in  Great  Britain,  and  the  total  receipts 
for  the  year  were  £28565355;  the  expenses  were  £878681 
less  than  the  net  receipts.  How  many  dollars  U.  S.  currency 
w^ere  the  net  receipts  per  mile,  sterling  bills  being  quoted  at 
189^? 

92.  The  number  of  men  sent  into  the  army,  up  to  Jar^  1, 
1863,  from  Illinois,  Ohio,  Pennsylvania,  and  New  York,  was 
proportional  respectively  to  the  numbers  27j^g,  34,  40  and 
44^  ;  Ohio  sent  34743  more  men  than  Illinois.  What  num- 
ber of  men  did  each  State  furnish  1 

93.  A  farmer  exchanged  25  bu.  3  pk.  3  qt.  of  corn  at  $.80 
per  bushel,  for  32  yds.  sheeting  and  8§  yds.  broadcloth.  Al- 
lowing 1  yd.  of  broadcloth  to  equal  in  value  24  yds,  of  sheet- 
ing, what  was  the  amount  paid  for  eachl 

94.  If  I  make  a  profit  of  15-j=\^  by  selling  Worcester's 
Dictionaries  for  $.85  above  the  cost,  how  much  must  I  ad- 
vance on  the  price  to  realize  a  profit  of  32^,^  ? 

95.  A  farmer  sold  4  loads  of  oats,  averaging  35  bu.  3  pk. 
7  qt.  each,  for  $120.85i.  How  much  are  100  bu.  3  pk.  worth 
at  the  same  rate? 

96.  Three  men  engaged  in  the  manufacture  of  pails ;  A  put 
in  $2550  for  8  months ;  B,  a  sum  not  specified  for  12  months ; 
C,  $1080  for  a  time  not  specified.  A  received  for  his  stock 
and  profit  $3400  ;  B,  $4200  for  his ;  C,  $1485  for  his.  Re- 
quired B's  stock  and  C's  time. 


ARITHMETICAL   EXAMPLES.  123 

97.  A  man  has  two  sons,  one  living  in  New  York,  the  other 
m  Massachusetts ;  he  wishes  to  place  at  interest  $1000  for 
each,  so  that  the  amounts  shall  be  the  same  in  5  yr.  7  mo. ; 
he  supposes  he  has  accomplished  his  object  by  loaning  the 
given  principals,  one  in  New  York  at  simple  interest ;  the 
other  in  Massachusetts  at  compound  interest,  payable  semi- 
annually. What  is  the  difference  between  their  respective 
amounts  1 

98.  Bought  42  lb.  of  coffee  at  the  rate  of  3 A  lb.  for  $1.00, 
and  75  lb.  more  at  the  rate  of  7  lb.  for  $2.33] ;  sold  the 
whole  at  the  rate  of  9  lb.  for  $3.25.  How  much  did  I  gain 
or  lose  1 

99.  If  7  cwt.  2  qr.  18  lb.  of  sugar  cost  $90.24,  how  much 
sugar  can  be  purchased  for  $300.80  ? 

100.  For  what  sum  must  a  store  and  contents,  valued  at 
$25640,  be  insured,  so  as,  in  case  of  its  destruction,  to  recover 
the  entire  value  of  the  building  and  contents  and  the  premium 
of  2  per  cent.  ? 

101.  A  person  traveled  from  New  York  to  Harrisburg  in 
12  days,  walking  4  miles  the  first  day,  6  miles  the  second,  8 
miles  the  third,  and  so  on.  How  far  is  Harrisburg  from  New 
York? 

102.  The  total  length  of  mail  routes  in  the  U.  S.,  June  1, 
1861,  was  140349  miles  ;  the  total  annual  transportation  was 
54455412  miles.  Allowing  that  no  mails  were  carried  on 
Sunday,  how  many  times  per  day,  on  an  average,  were  the 
mails  carried  over  each  route  1 

103.  A  commission  merchant  receives  125  bbls.  of  flour 
from  A,  150  bbls.  from  B,  225  bbls.  from  C;  he  finds  on  in- 
spection that  A's  is  10^  better  than  B's,  and  C's  is  5y\^  bet- 
ter than  A's ;  he  sells  the  whole  lot  at  $7.00  per  barrel, 
and  charges  4%  commission.  How  much  must  he  remit  to 
each  ? 

104.  A  man  sold  a  farm  of  165  A.  2  R.  32  P.  at  $33.50 


124  ARITHMETICAL    EXAMPLES. 

per  acre,  and  took  a  note  payable  in  5  mo.  15  da.,  at  7^  in- 
terest ;  wishing  the  money  for  immediate  use,  he  got  the  note 
discounted  at  a  bank.     How  much  did  he  receive  1 

105.  I  wish  to  line  the  carpet  of  a  room,  6  J  yd.  long  and  5J 
yd.  wide,  with  duck,  g  yd.  wade.  How  many  yds.  of  lining 
must  I  purchase,  if  it  will  shrink  4^  in  length  and  6%  in 
width  1 

106.  Bought  cloth  at  $4.00  per  yard.  What  must  be 
my  asking  price,  that  I  may  fall  on  it  12^,  and  still  make 
21%  on  my  purchase  ? 

107.  A,  B  and  C  engaged  in  partnership  with  a  joint  capi- 
tal of  $3000 ;  A  putting  in  stock  for  8  months,  B  for  9 
months,  C  for  12  months;  A's  part  of  the  profits  was  $64, 
B's  181,  and  C's  $84.     Required  the  capital  of  each. 

108.  What  is  the  net  value  in  Chicago  of  a  sum  due  in 
Paris  of  6300  francs,  which  is  sent  to  Liverpool,  at  1^  com- 
mission ;  exchange,  25.20  francs  to  £1  ;  a  draft  for  the  net 
amount  in  Liverpool  is  drawn  on  Boston  at  7^  premium,  after 
deducting  1%  commission  ;  the  proceeds  of  this  bill  being  re- 
mitted to  Chicago  in  a  check  at  1%  discount? 

109.  What  is  the  cash  balance  of  the  following  account  on 
Dec.  31,  at  7  per  cent.? 

James  Hanson. 


Dr. 


1850     I  ' 

Sept.   3  To  Sundries  |  478  j  36 

Oct,     2  "  Mdse.  on  3  mo.  I  255  :  37 

h    21  '  "      •'       "   3    "  1  375  I  26 

Nov  12  !  "      "       "  3    "  I    80  :  Of) 

Dec.  15  I  "  Sundries  1  148  I  76 


1859. 

Sept.  17 

By  Sundries 

"     20 

"    Cash  on  acct. 

Oct.      3 

"      "        " 

Nov.  17 

"       "        " 

Dec.   27 

"      "        " 

96  !  54 

200  00 

325  00 

50  00 

84  00 


110.  In  the  battle  of  Shiloh,  April,  1863,  4%  of  the  Federal 
army  engaged  were  slain  upon  the  field  ;  19 J^  were  wounded  ; 
and  the  prisoners  were  77  more  than  50^  of  the  wounded, 
also  2355  more  than  the  killed.  How  many  men  were  in 
the  engngement  ? 

111.  A  merchant  bought  64  yd.  broadcloth,  which  was  1| 
yd.  wide,  for  $5  per  yard ;    but  the  cloth  being  wet,  shrunk 


ARITHMETICAL    EXAMPLES.  125 

41  per  cent,  in  width,  a^nd  the  same  in  length.    For  what  niust 
the  cloth  be  sold  per  square  yard  to  gain  20  per  cent  1 

112.  The  population  of  the  United  States  in  1S60  was 
31446400,  and  the  number  of  deaths  reported  was  1  for  every 

80  citizens ;  -^  of  the  deaths  were  of  females.     How  many 

of  each  sex  died  during  the  year  ? 

113.  I  can  sell  a  certain  piece  of  property  for  $9000  cash, 
or  for  14750  payable  in  9  months,  and  $5200  payable  in  1 
year ;  how  much  shall  I  gain  by  accepting  the  second  offer, 
if  money  is  worth  9^  ? 

114.  A  gentleman  deposited  $100  in  a  savings  bank  for 
the  benefit  of  his  son,  at  compound  interest,  at  a  semi-annual 
rate  of  2}^% ;  he  was  to  receive  the  amount  as  soon  as  it  be- 
came $268.50 ;  allowing  that  the  deposit  was  made  when  the 
son  was  one  year  old,  what  was  his  age  when  he  received  the 
money '? 

115.  One-fifth  is  what  per  cent,  of  three-fourths  1 

116.  The  receipts  of  the  Post  Office  department  in  Ken- 
tucky for  the  year  ending  June  30,  1861,  were  as  follows: 
letter  postage,  $8029.59;  newspaper  postage,  $13981.36; 
registered  letters,  $388.00 ;  stamps  sold,  $136453.98.  The 
expenses  were  $59612.19  for  compensation  of  postmasters, 
$16423.14  incidentals,  $270273.23  for  transportation  of 
mails.  What  was  the  net  expense  to  the  Government  of 
carrying  the  mails  in  Kentucky  during  the  year  ? 

117.  I  exchanged  60  Ohio  State  bonds  of  liOOO  each,  at 
S.^%  premium,  for  Indiana  bonds  of  $200  each,  at  5^  pre- 
mium.    How  many  of  the  latter  did  I  receive  1 

il^.  If  12  oz.  of  wool  make  2|  yd.  of  cloth,  11  wido,  how 
many  pounds  of  wool  are  required  to  make  115  yds.  of  cloth 
1  yd.  wide  1 

119.  A  and  B  contracted  with  Gwinn  and  Co.  to  erect  a 
cotton-mill  for  $50000.     Not  wishing  to  be  burdened  with 


126  ARITHMETICAL   EXAMPLES. 

the  salary  of  a  book-keeper,  it  was  arranged  that  each  partner 
should  keep  a  strict  account  of  all  his  expenditures  and  re- 
ceipts, and  report  at  the  completion  of  the  job,  at  which  time 
they  w^ould  have  a  general  settlement.  At  the  time  of  set- 
lement  they  found  their  affairs  standing  as  follows,  viz. :  A 
had  paid  out  for  building  material  and  wages  $16750.50, 
and  had  received  from  Gwinn  &;  Co.  $12790;  B  had  paid 
out  for  building  material  and  wages  $20186.75,  and  had 
received  of  Gwinn  and  Co.  $15842.  There  was  due  the 
hands  and  for  material,  $4729.38.  What  was  their  entire 
profit ?  How  much  was  due  from  Gwinn  &  Co?  How 
much  should  be  paid  to  A  and  B  respectively  ? 

120.  Bought  a  bill  of  goods  for  $1500,  ]  payable  in  3 
months,  {  in  G  months,  and  the  remainder  in  9  months.  How 
much  ready  cash  ought  I  to  pay  for  the  goods,  money  being 
w^orth  6  per  cent.? 

121.  If  a  ship  sail  5  mi.  3  fur.  9^  rd.  per  hour,  how  long 
'will  it  be  in  going  1618  mi.  2  fur.  18.254  rd.  ? 

122.  A  house  that  cost  $15725,  rents  for  $1478.15;  the 
insurance  is  |  %,  and  the  repairs  j%%  each  year.  What  rate 
of  interest  does  it  pay  ? 

123.  A  merchant,  having  sold  a  number  of  yards  from  a 
piece  of  cloth,  found  there  were  8.75  yards  left,  which  was 
65  per  cent,  less  than  the  quantity  cut  off.  Required  the 
number  of  yards  in  the  piece  at  first. 

124.  The  capital  stock  of  the  Boston  and  Worcester  Rail- 
road Company  is  $4500000,  and  its  debt  $126000.  Its  gross 
earnings  in  1861  were  $928932,  and  its  expenses  $520338. 
If  the  company  paid  expenses,  interest  on  its  debt  of  6^,  and 
reserved  $18534,  what  dividend  would  a  stockholder  receive 
who  owned  25  shares  of  $100  ? 

125.  If  1990.73  gain  $55.67  in  9  mo.  19  da.,  what  princi- 
pal is  required  to  gain  $31.12  in  2  yr.  5  mo.  26  da.  ? 

126.  Find  a  number  between  893   and  931,  which  shall 


ARITHMETICAL    EXAMPLES.  12  J 

have  with  each  the  same  greatest  common  divisor  that  they 
have  with  each  other. 

127.  A  merchant  has  $210  due  him,  to  be  paid  in  7  months  ; 
hut  the  dehtor  agrees  to  pay  one-half  ready  money,  and  |  of 
the  remainder  in  6  months.  Wliat  time  should  he  be  allowed 
for  paying  the  balance  ? 

128.  Imported  from  Havre  120  baskets  of  champagne,  12 
bottles  each,  5^  breakage,  duty  40^,  freight  and  other  charges 
$134.10;  and  the  whole  cost  $1166.42.  How  much  did  it 
cost  per  bottle  m  Havre?  how  much  in  store?  and  what 
must  I  charge  per  bottle  to  clear  20^^  ? 

129.  How  much  butter  at  $.37^  a  pound,  must  be  given 
for  12  gal.  3  qt.  of  molasses,  at.  8.75  a  gallon? 

130.  The  paid-in  capital  of  the  United  States  Insurance 
Company  in  1863,  was  $879720;  its  receipts  for  the  year 
were  8314470  ;  and  its  losses  and  expenses  $138526.  What 
rate  of  dividend  could  it  declare  ? 

131.  How  many  feet  of  boards  will  it  take  to  inclose  a 
garden  '40  ft.  6  in.  long,  and  30  ft.  3  in.  wide,  with  a  close 
fence  7  ft.  6  in.  high  ? 

132.  A  pork  merchant  charged  12^  commission,  and 
cleared  $2251.30,  after  paying  out  $1565.24  for  all  expenses 
of  packing ;  if  the  pork  cost  him  $.06-^  a  pound,  how  many 
pounds  did  he  pack  ? 

133.  How  much  more  can  a  bank  make  in  528  days,  with 
$10000^y  discounting  notes  on  45  days'  time,  than  by  dis- 
counting them  on  30  days,  the  rate  of  discount  being  6^,  and 
the  profits  in  both  cases  retained  in  bank  till  the  expiration  of 
the  time  ? 

134.  Sold  Hiram  Jones  goods  to  the  amount  of  $2084,  on 
credit  for  6  mo.  from  Sept.  20,  1862 ;  Oct.  8  he  paid  me 
$520;  Nov.  20,  $340;  Dec.  25,  $800;  Jan.  12,  1863,  $100. 
When,  in  equity,  ought  I  to  receive  the  balance? 

135.  When  a  bill  on  Paris  for  28965  francs  costs  $7183.32, 
w^hat  per  cent,  is  the  rate  of  exchange  above  par  ? 


128  ARITHMETICAL    EXAMPLES. 

13G.  Tlio  average  dividends  of  all  the  savings  banks  in  Mass. 
in  18G1,  ^vere  4^%,  and  $1943532  was  distributed  among  the 
depositors.  What  were  the  aggregate  deposits  in  the  savings 
banks  ? 

137.  A  sells  goods  which  had  cost  $800,  to  B  at  an  ad- 
vance of  12^^;  B  sells  them  to  C,  and  gains  11^^  of  what  ho 
had  paid.  What  per  cent,  would  A  have  gained  had  he  sold 
the  goods  to  C  for  the  same  which  B  received  1 

1£8.  There  wa3  paid  in  New  Orleans  |7840  for  £1600  draft 
on  Liverpool.     At  what  per  cent,  premium  was  it  purchased  ? 

139.  If  it  require  |900  to  support  a  family  of  12  persons, 
41  weeks  and  1  day,  how  much  at  the  same  rate  will  be  re- 
quired to  support  a  family  of  24  pcr-ons  23  weeks  6^  days  ? 

140.  Subtract  2  fur.  10  rd.  5  yd.  2  ft.  fi-om  2  far.  11  rd. 
1  ft.  5  in. 

141.  The  Cleveland,  Columbus  and  Cincinnati  Railroad  re- 
ported it3  earnings  for  16G3  to  be  821450S0 ;  and  its  expenses, 
$961785 ;  the  company  invested  in  new  depots,  engineg,  cars 
and  railroad  stock,  $551739;  Aug.  1,  1SG3,  it  declared  a  Gfo 
dividend  of  its  paid-in  capital  of  1^5000000,  and  Jan.  1,  18G4, 
another  i>^  dividend.     What  surplus  revenue  still  remained  ? 

142.  The  stock  of  three  partners,  A,  B  and  C,  was  $2400, 
$2000,  and  $1800,  and  their  gain  $768,  $960,  and  $1152  re- 
spectively ;  C's  stock  continued  in  trade  4  months  longer  than 
B's.     How  long  Avas  the  money  of  each  in  trade  1 

143.  If  12^  of  what  is  received  for  goods  is  gaiif?  what  is 
the  gain  %  1 

144.  I  sold  I  of  ray  goods  at  an  advance  of  25^;  f^  of 
them  at  a  loss  of  8^  ;  37^5  of  them  at  a  profit  of  30^,  and  -J  of 
them  at  a  discount  of  20^.  For  what  ^  of  the  cost  must  the 
remainder  be  sold  in  order  to  lose  5^^  on  the  whole  1 

145.  The  charter  of  a  new  railroad  company  limits  the  stock 
to  $1500000,  of  which  3  installments  of  10^.  20^,  and  40^, 
respectively,  have  been  paid  in ;  the  cost  of  construction  has 


ARITHMETICAL    EX  A  TUPLES.  129 

reached  -S850000,  and  the  estimated  cost  of  completion  is 
$850000.  If  the  company  call  m  the  final  installment  of  \U 
stock,  and  assess  the  stockholders  for  the  remaining  outlay, 
what  will  be  the  rate  %  1 

140.  At  the  surrender  of  Island  No.  10,  the  privates  taken 
were  60^  of  the  number  of  arms  taken;  the  line  officers  were 
34^  of  the  privates,  and  the  field  officers  and  generals,  30  in 
number,  were  -\  %  of  the  privates.  How  many  privates,  and 
what  number  of  arms  were  captured  ? 

147.  The  greatest  common  divisor  of  three  numbers  is  18, 
each  of  the  numbers  exceeds  18,  and  their  least  common 
multiple  is  540.     What  are  the  numbers  ? 

148.  If  9T  sheep  are  bought  for  SlOOrf,  how  much  should 
be  paid  for  25  sheep  at  the  same  rate  ? 

149.  I  sold  goods  at  an  advance  of  20^,  and  invested  the 
money  received  in  goods  which  I  sold  at  a  loss  of  10^,  and 
with  the  sum  received  purchased  goods  wliich  were  sold  at  a 
discount  of  16§^.     What  was  the  gain  or  loss  per  cent.  ? 

150.  Borrowed  of  my  neighbor  $500,  for  1  yr.  3  mo.,  at 
Q% ;  not  being  able  to  pay  at  the  end  of  the  time,  my  neigh- 
bor agreed  to  let  it  run  till  the  end  of  the  second  year  at 
simple  interest,  but  he  was  obliged  to  borrow  $535.88]  for  9 
mo.  at  the  same  rate.  How  much  more  did  my  neighbor 
ov/e  at  the  end  of  the  year  than  I  ? 

151.  The  earth  moves  19  miles  per  second  in  her  orbit. 
How  far  does  she  travel  fi-om  7  h.  30  min.  A.  M.  till  5  h.  15 
miu.  P.  M.  ? 


lo2.    $1000.  CoLLixsviLLE,  Conn.,  Mar.  1,  1863. 

Six  months  after  date  I  promise  to  pay  James  Gray,  or 
order,  one  thousand  dollars,  for  value  received. 

T.  M.  CURTISS. 

On  this  note  were  the  following  indorsements:  Sept.  1, 
1863,  $300;  Jan.  16,  1864,  $200;  March  1,  1864,  $200; 
Mr.y  1,  1864,  $200.     How  much  was  due  Julv  4,  18641 

C* 


130  ARITHMETICAL   EXAMPLES. 

153.  The  Milwaukee  and  Prairie  du  Chieii  Railroad  report- 
ed, for  the  year  1863,  gross  earnings,  11184840 ;  total  ex- 
penses, $793747  •  the  interest  on  sinking  fund  was  $204480, 
and  $31613  was  expended  for  various  items  of  construction; 
the  balance  was  a  5^  dividend  on  the  capital  stock.  Required 
the  capital  stock. 

154.  Having  used  my  carriage  three  years,  I  sold  it  for 
$Q6,  which  was  40^  less  than  the  cost.     What  was  the  cost  ? 

155.  What  is  the  value  of  25  hhd.  sugar,  each  weighing  12 
cwt.  3  qr.  ]6  lb.;  draft,  3  lb.  per  cwt.,  and  tare  10  lb.  per 
cv;t.,  at  $11,625  per  cwt.  net? 

156.  A  man  having  $28^,  gave  |  of  it  for  5|  bushels  of 
clover  seed.     What  was  the  price  per  pound  1 

157.  A  merchant  imported  from  Bremen  40  pieces  of 
linen  of  35  yards  each,  on  which  he  paid  for  duties,  at  26^, 
$218.40,  and  other  charges  to  the  amount  of  $131.60.  What 
was  the  invoiced  value  per  yard  ?  and  the  cost  per  yard  after 
duties  and  charges  were  paid  1 

158.  At  the  battle  of  Fredericksburg,  Dec.  13,  1862,  the 
losses  of  the  Federal  army  in  killed,  wounded  and  prisoners, 
were  in  the  proportion  of  12, 22  and  97  respectively,  and  there 
were  1 990  more  prisoners  than  killed.    Required  the  total  loss. 

159.  How  many  sacks  of  coffee,  each  containing  108  lb.,  at 
Is.  6d.  per  pound.  New  York  currency,  v/ill  pay  for  135 
yards  of  broadcloth,  at  $3|  per  yard? 

160.  A  buyer  expended  equal  sums  of  money  in  the  pur- 
chase of  wheat,  rye  and  oats ;  in  the  sales  he  cleared  7^^  on 
the  wheat,  5%  on  the  rye,  but  lost  15^  on  the  oats ;  the  whole 
amount  received  was  $1782.  What  sum  did  he  expend  for 
each  kind  of  grain  ? 

161.  I  received  an  S%  dividend  on  New  York  city  railroad 
stock,  and  invested  the  money  in  the  same  stock  at  80^.  My 
stock  having  incroaced  to  $13750,  what  was  the  amount  of 
my  dividend 


ARITHMETICAL    EXAMPLES.  131 

162.  Great  Britain  and  Ireland  have  an  area  of  112100 
square  miles,  and  a  population  of  29169400.  Supposing  the 
families  to  average  5  persons,  and  the  whole  area  to  be  equally 
divided  among  them,  how  much  land  couid  each  flimily  pos- 
sess"? 

163.  If  molasses  cost  20^  less  than  $.75  a  gallon,  and  it 
be  sold  at  a  profit  of  25^^,  at  what  price  is  it  sold  ? 

161.  The  quick  step  in  marching  being  2  paces  of  28 
inches  each,  per  second,  what  is  the  rate  per  hour  ? 

165.  How  much  time  must  a  general  allovr  for  a  detach- 
ment of  soldiers,  marching  quick  step,  to  reach  a  place  50 
miles  distant,  giving  the  men  a  halt  of  1^  hours? 

166.  A  capitalist  holding  bonds  of  the  Columbus  and 
Indianapolis  Railroad,  to  the  amount  of  827000,  exchanged 
them  at  the  market  price  of  96^,  for  capital  stock  of  the  same 
company,  worth  81^;  the  bonds  drew  S%  annually,  while  the 
stockholders  received  two  dividends  during  the  year ;  the  first 
of  3A  %j  and  the  second  of  4^.  How^  much  did  the  capitalist 
gain  annually  by  the  exchange  ? 

167.  The  population  of  Mass.  in  1850  was  994500;  in 
1860,  1131191;  of  Penn.  in  1850,  2311800,  and  in  1860, 
2901309.  How  much  more  w^as  the  increase  per  cent,  in 
Penn.  than  in  Mass.  for  the  ten  years  1 

168.  If  the  interest  of  $6786.24  for  1  yr.  1.0  mo.  16  da.  is 
SI 273.89,  what  will  be  the  amount  of  $5772  from  Oct.  26, 
1859,  to  Apr.  12,  1864? 

169.  Find  the  day  of  maturity,  the  time  to  run,  and  the 
proceeds  of  the  following  note: 

c^^'jK  6  3  Chicago,  M;ircli  2,  ISG-i. 

Six  months  after  date,  I  promise  to  pay  to  the  order  of 
Marks  &  Willis,  five  hundred  seventy-five  -f'^f^  dollars,  value 
received. 

Hiram  Bennet, 
Discounted  at  a  bank,  Apr.  10^,  at  6j^. 


132  ARITHMETICAL    EXAMPLES. 

170.  If  8  men  can  perform  a  piece  of  work  in  32  days, 
how  many  men  must  be  added  to  the  number  to  perform  the 
work  in  8  days  ? 

171.  The  total  value  of  all  the  property,  real  and  personal, 
of  the  Free  States  in  18G0,  was  810852081600;  and  of  the 
Slave  States,  $5225307000.  The  products  of  the  Free  States 
for  the  sam.e  year  were  valued  at  $4178051416  ;  of  the  Slave 
States,  $1149567540.  How  much  greater  per  cent,  of  the 
capital  invested,  were  the  products  of  the  Free  States,  than  of 
Slave  States? 

172.  In  what  tima  will  any  sum  of  money  amount  to  10 
times  itself  at  7  per  cent.  ? 

173.  A  merchant  sold  a  quantity  of  goods  for  $480,  and 
loses  at  the  rate  of  9  per  cent.  What  ought  he  to  have  sold 
them  for  to  realize  a  profit  of  7  per  cent.  ? 

174.  If  a  man  dig  a  cellar  8  feet  square  and  6  feet  deep  in 
2  days,  how  long  will  it  take  him  to  dig  a  similar  one  12  feet 
square  and  7  feet  deep  1 

175.  The  cost  in  store  of  40  puncheons  of  Jamaica  rum.,  84 
gal.  each,  was  $1262.86;  duty  15f^;  leakage  2%^  and  charges 
$106.68.     What  was  the  cost  per  gallon  in  Jamaica  ? 

176.  In  the  examination  of  a  class,  160  questions  were  sub- 
mitted to  each  of  the  five  members ;  A  answered  130 ;  B, 
125;  C,  115;  D,  122;  and  E,  158.  V\^hat  was  the  standing 
of  the  class  ? 

177.  If  an  army  of  5000  men  have  provisions  for  15  days, 
at  the  rate  of  20  oz.  a  day  to  each  man,  and  they  be  reinforced 
with  3000  men,  upon  what  daily  allowance  must  each  man  be 
put  that  the  same  provision  may  last  20  days  1 

178.  The  British  Industrial  Exhibition  remained  open  141 
days,  and  the  average  numiber  of  daily  visitors  was  42831  ; 
the  whole  amount  received  for  admission  was  £6039171. 
What  was  the  price  of  admission? 

179.  What  per  cent,  of  24^  is  4  of  54^? 


ARITHMETICAL    EXAMPLES.  166 

180.  A  liquor  dealer  receives  an  invoice  of  800  dozen  bot- 
tles of  porter,  rated  at  81.50  per  dozen;  allowing  2%  for 
breakage,  what  will  be  the  duty  at  24% '? 

ISl.  If  the  transportation  of  8  lihd.  sugar,  each  weighing 
121  cwt.  25  leagues,  cost  865,  what  must  be  paid  for  the 
transportation  of  80  tierces  of  2^  cwt.  each,  75  leagues  ? 

182.  I  wish  to  obtain  at  a  bank  $840.25  ;  for  what  sum 
must  I  give  my  note  payable  in  5  months  and  21  days  ? 

183.  A  portion  of  a  cargo  of  tea  being  damaged,  was  sold 
at  $1.20  per  pound,  and  at  a  loss  of  161%.  -^^  what  rate 
must  the  remainder  be  sold  to  gain  25^^  1 

184.  A  merchant  bought  2  pieces  of  goods  containing  60 
yds.  each,  at  ^.75  a  yard ;  he  also  paid  |  of  a  cent  per  yard 
for  freight.  For  what  must  he  sell  the  goods  per  yard  to  make 
a  profit  of  25^,  if  the  pieces  fall  short  in  measuring  21%  1 

185.  A  person  j^aid  a  tax  of  5  per  cent,  on  his  income. 
What  must  his  income  have  been  if,  after  he  had  paid  the  tax, 
there  was  85671.50  remaining'? 

186.  If  11  lb.  of  cheese  are  equivalent  in  value  to  7  lb.  of 
meat,  and  21  lb.  of  meat  to  4  bu.  of  corn,  and  20  bu.  of  corn 
to  22  bu.  of  rye,  and  0  bu.  of  rye  to  2  cords  of  wood,  how 
many  pounds  of  cheese  must  be  given  in  exchange  for  12 
cords  of  v/ood  ? 

187.  What  is  the  compound  interest  of  $512.50  for  3  yr. 
6  mo.  21  da.,  at  S%  1 

188.  A  store  and  its  goods  are  w^orth  $12740.  What  sum 
must  be  insured  at  2%  to  cover  both  property  and  premium  1 

189.  The  value  of  flour  and  meal  produced  in  the  United 
States,  in  1860,  was  $225000000  ;  of  cotton  during  the  same 
year,  $115500000.  The  value  of  cotton  was  what  %  of  the 
value  of  the  flour? 

190.  How  many  square  feet  in  the  four  walls  of  a  room  36 
ft.  long,  SO  ft.  wide,  and  10!  high? 

191.  A  merchant  sold  flour  at  $6.50  per  barrel,  and  gained 


134  ARITHMETICAL    EXAMrLES. 

10^;  he  afterwards  sold  the  same  khid  of  flour  at  '1^8.25  per 
barrel.     AVhat  per  cent,  did  he  gain  at  the  latter  p;uce  1 

192.  How  shall  a  merchant  tailor  mark  coats  that  cost 
18.00  so  as  to  fall  20;^  from  the  marked  price,  and  yet  make 
2~i^o  on  the  coats  ? 

193.  What  must  2]  lb.  of  tea  be  sold  for,  if  221  lb.  cost 
$14,  and  the  retail  profit  is  20;^] 

194.  The  area  of  Ehode  Island  is  519698  acres,  the  cash 
value  of  which  in  1860  was  119488675  ;  the  area  of  Delaware 
is  1004295  acres,  of  which  the  cash  value  was  $31420357 ;  at 
the  same  time  there  were  2290  slaves  in  Delaware.  Now,  if 
by  freeing  the  slaves  in  the  latter  State  the  cash  value  of  the 
farms  would  become  the  same  per  acre  as  in  Ehode  Island, 
how  much  would  the  State  gain,  reckoning  the  slaves  at  an 
average  value  of  1250  ? 

195.  I  of  28  is  j\  of  how  many  ^  of  55  ? 

196.  A  man  owed  $420,  due  Oct.  1,  1863;  he  payed  part 
of  it,  Aug.  15,  1863,  and  the  rest  Jan.  1,  1864.  What  were 
the  payments  1 

197.  If  372  men  in  7|  days,  of  11  hours  each,  dig  a  canal  of 
7  degrees  of  hardness,  310  yards  long,  5A  yards  wide,  and  21 
yards  deep,  in  how  many  days,  of  8  hours  each,  will  27  men 
dig  a  canal  of  4  degrees  of  hardness,  270  yards  long,  7  yards 
wide  and  o\  yards  deep  *? 

198.  The  net  proceeds  of  the  sale  of  1000  tons  of  hay,  at 
$20  per  ton,  after  deducting  $875  for  charges,  were  $18325. 
What  rate  of  commission  was  charged  ? 

199.  What  principal  will  gain  $213,  at  7J  per  cent.,  in  2 
yr.  4  mo.  12  da.? 

200.  The  area  drained  by  the  ponds  and  lakes  which  sup- 
ply the  city  of  Brooklyn  with  water  is  62:i  square  miles, 
upon  which  the  average  annual  fill  of  rain  is  381  inches  ;  the 
average  daily  supply  to  the  city  is  20000000  gallons.  How 
much  water  falls  for  every  gallon  conveyed  to  the  city  ? 


ARITHMETICAL    EXAMPLES.  135 

201.  What  is  the  least  common  multiple  of  G-A,  9|,  10| 
and  T/e  ^ 

202.  An  army  which  has  been  three  times  decimated  in 
battle  now  numbers  only  14580  men.  What  was  the  origi- 
nal number  in  the  army  ? 

203.  Sold  2978  bushels  of  wheat  at  $2.00  per  bushel  ;  in- 
vested the  proceeds  in  sugar,  as  per  order,  reserving  my  com- 
mission of  5^  for  selling  and  H^  for  buying,  and  the  expense 
of  shipping,  $53.37.     How  much  did  I  invest  in  sugar  ? 

204.  A  and  B  had  the  same  amount  of  money ;  A  spent 
76%  of  his  money  for  land,  and  B  lost  b}^  gambling  a  sum 
equal  to  28^-5^  of  what  both  had  at  first,  when  both  together 
had  $50.25.  What  sum  had  each  at  first,  and  how  much  had 
each  left  1 

205.  There  are  20  colleges  in  New  York,  having  an  aggre- 
gate of  118060  volumes  in  all  their  libraries.  What  is  the 
average  value  of  these  libraries,  at  8|  per  volume  1 

206.  What  per  cent,  of  a  number  is  40^  of  |  of  it  1 

207.  How  far  does  a  man  walk  in  planting  a  field  of  corn 
207  ft.  square,  the  rows  being  3  feet  apart  and  3  feet  from 
the  fence  1 

208.  A  merchant  owes  $440,  payable  in  20  months,  and 
S896,  payable  in  24  months ;  the  first  he  pays  in  5  months, 
and  the  second  in  one  month  after  that.  How  much  should 
he  pay,  allowing  8  per  cent,  per  annum  1 

209.  Willis,  Markham,  &  Co.  of  New  Orleans  import  from 
Liverpool  8  pieces  of  Turkey  Carpeting,  35  yd.  each,  at  6s. 
per  yd.,  duty  33]^;  300  yd.  woolen  goods  at  4s.  per  yd., 
duty  18^,  and  25  pieces  of  silk,  18  yds.  each,  at  2s.  6d.  per 
yard,  duty  24^.  Required  the  whole  amount  of  duty,  allow- 
ing the  value  of  the  pound  sterling  to  be  $4.84  ? 

^  210.  Paid  $63.90  duties  at  the  rate  of  9  per  cent,  on  50 
casks  of  raisins,  tare  15  lb.  per  cask  ;  allowing  the  gross 
weight  of  each  cask  to  have  been  115  lb.,  what  was  the  in- 
voice value  per  pound  1 


136  ARITHMETICAL    EXAMPLES. 

211.  The  total  value  of  real  estate  and  personal  property 
in  California  in  1850  was  $22161872  ;  in  i860,  |207874('!l.5 
What  was  the  total  increase,  and  increase  per  cent.  ? 

212.  Divide  1435  among  A,  B,  and  C,  so  that  ^  of  A's 
money  shall  be  equal  to  ^  of  B's,  or  |  of  C's. 

213.  James  Haynes  buys  a  bill  of.  merchandise  in  New 
York,  at  cash  price,  to  the  amount  of  $2973.80,  and  gives  in 
payment  his  note  at  3  months  at  7^^.  What  must  be  the 
face  of  the  note  ? 

214.  If  6  men  do  as  much  w^ork  as  14  women,  and  10 
women  as  much  as  27  boys,  and  14- boys  as  much  as  25  girls, 
and  18  girls  bind  250  sheaves  in  an  hour,  how  many  sheaves 
can  24  men  bind  in  the  same  time  ? 

215.  If  A  owes  1500  due  in  6  months,  |400  due  in  4 
months,  and  1300  due  in  7  months,  and  pays  |  of  the  whole 
in  3  months,  when  ought  the  remainder  to  be  paid  ? 

216.  The  population  of  Charleston,  S.  C,  in  1850  was 
42982,  and  in  1860,  40575;  the  population  of  New  Haven, 
Conn.,  at  the  same  dates  was  20345,  and  39266,  respectively. 
What  was  the  increase  per  cent,  in  New  Haven,  and  what  the 
loss  per  cent,  in  Charleston,  during  this  time  1 

217.  The  interest  of  $4000  for  1  month  and  6  days  is  |36, 
what  is  the  rate  per  cent. 

218.  Yfilliam  Hatch,  born  Feb.  29,  1844,  received  from 
his  father  a  present  of  $50  on  each  birthday  till  he  became  of 
age.     What  w*as  the  amount  received  ? 

219.  If  I  of  a  hogshead  of  oil  is  worth  $48,  what  is  the 
value  of  §  of  the  remainder  1 

220.  Bought  a  quantity  of  wine  for  675.32A,  at  $.85  per 
gallon  ;  but  a  part  having  leaked  out,  the  remainder  was  sold 
at  40^  advance,  and  the  original  cost  was  realized.  What 
quantity  leaked  out  ? 

221.  In  1860  there  were  7766  manufacturing  establish- 
ments in  Massachusetts,  with  an  aggregate  capital  of  $133- 


ARITHMETICAL    EXAMPLES.  137 

000000;  these  establishments  employed  210000  hands,  and 
consumed  during  the  year  $140000000  worth  of  raw  ma- 
terial, v.hich,  when  mannfoctured,  increased  in  value  to 
826G000000.  How  much  did  each  dollar  of  capital  produce  ? 
each  dollar  of  raw  material  ?  and  what  was  the  average  value 
produced  by  each  hand  ] 

222.  Bought  of  M.  J.  &  Co.  as  follows  :' 

April     1,  1863,  on  60  days'  credit,  a  bill  of  $250 
"      20,     "        "    90      "  "  "  600 

July       5,     "        "   SO      "  "  "  400 

Also,  sold  to  M.  J.  &;  Co. : 

April      5,  1863,  on  2  months'  credit,  a  bill  of  $450 
May     20,     "       "   3         "  "  ''•  600 

From  what  date  ought  the  balance  of  the  debt  to  dravf  inter^ 
est? 

223.  Gave  my  note  at  a  bank  for  ^'12">5.^^8,  payable  in  4 
mo.  12  da. ;  if  discounted  at  6^,  what  sum  did  I  receive  ? 

224.  A  merchant  sold  goods  for  8600,  and  gained  25^ ; 
he  invested  the  proceeds  in  flour,  on  which  he  lost  20^  ;  did 
he  gain  or  lose  by  the  transaction  1  and  how  much  ? 

225.  Four  per  cent,  of  325  bushels  is  what  per  cent,  of  3J 
per  cent,  of  200  bushels  ? 

226.  A  owes  B  $600  due  in  4  months,  and  $840  due  in  6 
months ;  B  owes  A  $1600  due  in  7  months.  If  A  should 
make  present  payment  of  his  debts,  wlien  ought  B  in  justice 
to  pay  A  1 

227.  The  manufacturing  establishments  in  all  the  Southern 
States  in  1860  numbered  1806,  in  which  $100655000  capital 
was  invested;  these  establishments  emplo\'ed  110110  hands, 
and  consumed  $82609000  worth  of  raw  material ;  the  pro- 
ducts for  the  year  were  valued  at  $145360260.  How  much 
did  each  dollar  of  capital  produce  ?  each  dollar  of  raw  ma- 
terial ?  and  what  was  the  average  value  produced  by  each 
hand  ? 


138  ARITHMETICAL    EXAMPLES. 

228.  Bought  a  number  of  bales  of  velvet,  each  containmg 
126  yards,  at  the  rate  of  $10  for  7  yards,  and  immediately 
sold  the  whole  at  the  rate  of  $13  for  9  yards,  thereby  making 
126.     Kequired  the  number  of  bales? 

229.  If  eggs  are  bought  at  the  rate  of  10  for  $.25,  and  sold 
at  the  rate  of  6  for  $.16,  how  many  dozen  must  be  sold  to 
gain  $20  ] 

230.  In  what  time  at  12^  will  $240  amount  to  $720  ? 

231.  I  have  $58650  to  invest,  and  can  buy  New  York  Cen- 
tral 6's  at  102^,  or  New  York  Central  7's  at  115^.  How 
much  more  profitable  will  the  latter  investment  be  than  the 
former  per  year  ? 

232.  In  1862  there  were  88  instructors  in  Harvard  Univer- 
sity, and  the  ratio  of  teachers  to  students  was  1  to  22 ;  of 
teachers  to  alumni,  1  to  189 ;  of  alumni  to  the  volumes  in  the 
library,  9  to  190.  Required  the  number  of  students,  alumni, 
and  volumes  in  library. 

233.  One  thousand  dollars  was  to  be  divided  amono;  A,  B 
and  C,  in  the  ratio  of  ^,  |  and  |,  but  C  relinquished  his  share  ; 
how  much  did  A  and  B  each  receive  ? 

234.  A  wholesale  merchant  sent  a  quantity  of  goods  into 
the  comitry  to  be  sold  at  auction,  on  a  commission  of  4A^. 
What  amount  of  goods  must  be  sold,  that  his  agent  may  buy 
produce  with  the  avails  to  the  amount  of  $1910.  after  retain- 
ing a  commission  of  2%  % 

235.  How  many  yards  of  cloth,  IJ  yards  wide,  are  required 
for  a  garment  containing- 23  square  yards,  if  the  cloth  m  being 
sponged  shrinks  10^  in  length  and  8^  in  widtii? 

236.  The  products  of  Rhode  Island  in  1860,  were  valued  at 
$52440000,  or  $300  per  capita;  of  Delaware,  $16159000,  or 
$143  per  head.  What  was  the  difference  in  population  in  the 
two  States'? 

237.  If  I  of  A's  money  equals  ^  of  B's,  what  part  of  B's 
money  equals  |  of  A's  1 


ARITHMETICAL   EXAMPLES.  139 

238.  What  are  the  proceeds  of  a  note  of  $5600,  payable  in 
6  months,  discounted  at  7|^  ? 

239.  If  the  annual  rent  of  23  A.  1  R.  27  P.  of  land  be 
$187.35,  how  much  will  be  the  rent  of  71  A.  20  P.? 

240.  The  Julian  Calendar  assumed  the  year,  365  da.  6  h., 
instead  of  365  da.  5  h.  48  min.  49.7  sec,  its  true  length.  In 
how  many  years  was  1  day  gained  ? 

241 .  I  got  a  note  of  $800,  payable  in  4  months,  discounted  at 
a  bank  at  6^,  and  put  the  money  received,  upon  interest  at  the 
rate  of  7i^.  When  the  note  became  due  I  renewed  it  for  5 
months  by  paying  the  discount,  and  when  this  note  became  due 
I  renewed  it  as  before  for  such  a  time  that  it  became  due  in 
one  year  from  the  date  of  the  original  note,  at  which  time  I 
collected  the  sum  due,  and  paid  the  bank  no.e.  What  did  I 
gain  by  the  transaction  ? 

242.  If  the  interest  of  £179  12s.  lid.  for  1  yr.  7  mos.,  is 
£14  4s.  5{d.,  what  is  the  rate  per  cent.  1 

243.  Three  persons  found  $120,  which  they  agreed  to  share 
in  the  proportions  of  5,  ^7  and  8.  How  much  did  each  re- 
ceive? 

244.  A  commission  merchant  sold  goods  to  the  amount  of 
$59376.50,  for  which  he  charged  a  commission  of  |  of  one  per 
cent.     What  was  his  commission  ? 

245.  The  public  debt  of  the  United  States.  March  1,  1864, 
was  as  follows:  Immediate  Liabilities,  ^48725728.68;  Old 
Public  Debt,  $67447412.55;  7-30  Bonds,  $138772300;  U. 
S.  Notes,  $449119548.10;  Fractional  Currency,  $187457-:20.- 
15;  Twenty  Years  Loans  and  Bonds,  $51227000;  Treasury 
Notes,  $101362031.22;  Oregon  War  Debt,  $1016000;  Cer- 
tificates of  Indebtedness,  $136121650  ;  and  5-20  Bonds  $5i0: 
165446.92;  the  amount  in  the  Treasury  being  $9411795.27, 
what  was  the  debt  ? 

246.  A  has  $12000  loaned  in  Connnecticut,  and  $10600 
loaned  in  New  York.  On  which  sum  is  the  legal  interest  the 
greater,  and  how  much  per  year  1 


140  ARITHMETICAL   EXAMPLES. 

247.  A  man  took  out  a  life  policy  for  $3000,  at  the  rate  of 
121.50  per  $1000.  What  sum  must  he  deposit  in  a  savings 
bank,  the  compound  interest  of  which  at  5^,  payable  semi- 
annually, shall  discharge  his  annual  premium  1 

248.  A  merchant  bought  500  barrpls  of  flour  at  $6.50  a 
barrel,  and  sold  it  immediately  at  $7.25  a  barrel,  receiving  in 
payment  a  note  duo  three  months  hence,  which  he  had  dis- 
counted at  a  bank  afr6^.     What  did  he  gain  on  the  flour  1 

249.  If  a  staff  2  ft.  9  in.  long,  cast  a  shadow  1  ft.  1  ^  in., 
what  is  the  hight  of  a  pole  which  casts  a  shadow  63  ft.  1 

250.  The  gross  earnings  of  the  Michigan  Southern  Railroad, 
for  the  year  ending  March  1,  18G4,  were  $3308011  ;  the  ex- 
penditures, $1669006.  It  paid  interest  to  the  amount  of 
$690000,  and  a  10^  dividend  upon  its  preferred  stock  of 
$2893600.     How  much  remained  for  a  sinking  fund  1 

251.  If  ;}  of  a  ton  of  coal  be  sold  for  what  §  of  it  cost,  what 
is  the  gain  per  cent.  ? 

252.  A's  money  is  to  B's  as  3  to  4;  i  of  A's  money  placed 
at  interest  for  3  yr.  8  mo.  15  da.,  at  6  per  cent,  will  amount 
to  $418,095.     How  much  money  has  each  ? 

253.  Sold  wheat  at  $1.64  j-f  per  bushel,  and  gained  12^. 
For  what  should  it  have  been  sold  to  have  lost  15^^? 

254.  What  is  the  cost  of  a  90  days'  bill  on  Philadelphia,  to 
the  amount  of  $1000,  at  |^  premium,  and  interest  oft"  at  6^1 

255.  The  interest  of  a  certain  sum  for  1  mo.  19  da.  at  13^ 
per  cent,  is  $.866.     What  is  the  principal '? 

256.  The  Illinois  Central  Railroad  sold  in  one  month  26780 
acres  of  land  at  an  average  price  of  $10.95  per  acre,  and  an 
averao-e  credit  of  3  yr.  6  mo.  What  was  the  cash  value  of 
the  sales,  money  being  worth  6^? 

257.  A  and  B  are  partners ;  A's  stock  is  to  B's  as  5  to  8 ; 
after  4  months  A  withdraws  |  of  his,  and  B  |  of  his.  How 
shall  the  year's  gain,  $920,  be  divided  ? 


ARITHMETICAL    EXAMPLES. 


141 


258.  If  a  garden  of  a  certain  length  and  4  rd.  8  ft.  3  in. 
■wide  contain  ^  of  an  acre,  how  much  ^YOuld  it  contain  if  it 
were  9  rods  wide  1 

259.  When  is  the  balance  of  the  following  account  due,  per 
average "? 


Charles  Derby. 


Dr. 


Cr. 


1859.     1 

.. 

1S59. 

, 

— ■ 

Jan.    21   1 

To  Mdse. 

32 

00  1 

Jan.        1 

By  Cash, 

1     84 

00 

Mar.     5  1 

145 

00  ! 

Feb.        4 

44         44 

40 

00 

"     22 

U           i( 

194 

00  i 

Mar      30 

"         " 

li 

00 

260.  A  owed  82520,  due  July  18,  1863;  he  paid  8720  be- 
fore, and  the  rest  after  it  became  due.  When  were  the  pay- 
ments made  if  they  were  49  days  apart '? 

261.  If  8500  dollars  is  deposited  for  a  child  at  birth,  at  7^ 
compound  interest,  payable  semi-annually,  what  v/ill  it 
amount  to  when  the  child  is  21  years  of  age  1 

262.  Bought  fish  at  86.37^  per  quintal,  and  sold  the  same 
at  87.39^-.     What  was  the  gain  per  cent.  ] 

263.  The  amount  of  specie  in  Sub-Treasury,v  New  York, 
Feb.  1,  1864,  was  839963000;  during  the  month  two  steam- 
ers  from  California  brought  in  81250069;  888150  was  im- 
ported from  foreign  ports,  and  84825748  was  gathered  in 
from  hoarded  specie ;  the  amount  of  gold  exported  for  the 
same  time  was  83015367.  How  much  remxained  in  the  Sub- 
Treasury,  March  1,  1864? 

264.  J.  S.  Sanborn  purchased  80  acres  of  land  of  the  Illi- 
nois Central  Railroad  Company,  on  the  following  terms : 
Cash  payment,  848 ;  payment  at  the  end  of  the  first,  second 
and  third  years,  848  each ;  payment  at  the  end  of  the  fourth 
year,  8236 ;  at  the  end  of  the  fifth  year,  8224;  at  the  end  of 
the  sixth  year,  8212 ;  and  at  the  end  of  the  seventh  year, 
$200.     What  was  the  cash  price  per  acre  ? 

265.  Bought  a  watch  for  860,  and  sold  it  for  8100.  What 
per  cent  of  the  cost  was  the  gain  ? 

266.  If  3  pounds  of  tobacco  cost   8.84,  and  5  pounds  to- 


1^  ARITHMETICAL   EXAMPLES. 

bacco  are  worth  10^  pounds  of  sugar,  -vvhat  will  90  pounds  of 
sugar  cost  ? 

267.  AVhat  must  be  paid  in  Boston  for  a  draft  on  New 
York  at  30  days,  for  $4500,  exchange  being  at  ^^  premium  ? 

2G8.  The  cost  of  producing  fine  salt  at  the  Onondaga  Salt 
Works,  is  11}  cents  per  bushel,  and  coarse  salt  5  cents;  in 
1862,  1884697  bushels  of  coarse,  and  5315694  bushels  of  fine 
salt  were  produced,  and  sold  at  an  average  price  of  19  cents 
per  bushel.     What  was  the  per  cent,  of  profit  1 

269.  At  what  rate  must  a  note,  payable  in  one  year,  with- 
out grace,  be  discounted  to  produce  6^  interest  ? 

270.  The  factors  of  a  certain  number  are  16|,  30|,  and 
19| ;  what  is  |  of  |  of  J  of  the  number  ? 

271.  A  bank  has  $20000  loaned  on  call  at  5%',  how  much 
is  the  daily  interest,  reckoning  365  days  in  a  year  ? 

272.  Bought  a  horse  for  $110;  for  how  much  must  he  be 
sold  to  gain  37^^  1 

273.  The  total  value  of  real  estate  and  personal  property 
in  the  United  States  in  1850  was  $7135780228;  in  1862, 
$16159616068.  What  was  the  actual  increase  in  property  1 
and  the  increase  per  cent,  in  12  years  ? 

274.  A  man,  engaged  in  business  with  a  capital  of  $25000 
is  making  10^  per  cent,  per  annum  on  his  capital ;  but  on 
account  of  failing  health,  he  is  obliged  to  quit  business,  and 
loan  his  money  at  7  per  cent.  How  much  does  he  lose  in  2 
yr.  7  mo.  20  da.  ? 

275.  If  one  cubic  foot  of  anthracite  coal  weighs  56  lb.,  what 
must  be  the  length  of  a  bin  8  ft.  wide  and  6  ft.  deep,  to  hold 
14  long  tons  of  coal  ? 

276.  A  and  B  invested  equal  sums  in  trade ;  A  lost  20^ 
of  his  money,  and  B  gained  $50.05 ;  A's  money  was  then 
75^  of  B's  ;  what  sum  did  each  invest  ? 

277.  In  what  time  will  $4500  gain  $181.25  at  5  per  cent.  ? 


ARITHMETICAL   EXAMPLES.  143 

278.  A  merchant  bought  goods  in  Chicago  to  the  amount 
of  $850,  and  gave  his  note,  July  1,  1860,  on  interest  after  2 
months ;  4  months  after  the  note  was  given,  he  paid  $400, 
and  6  months  after  the  first  payment,  he  paid  $360.  What 
was  there  due  Sept.  19,  1862  ? 

279.  Iowa  produced  in  one  year  18350000  bushels  of 
wheat,  valued  at  $7200000;  60000000  bushels  of  corn,  worth 
$.12  per  bushel ;  10000000  bushels  of  oats,  valued  at  $1500- 
000 ;  3000000  bushels  of  potatoes,  worth  $.25  per  bushel. 
Required  the  whole  number  of  bushels  and  their  total  value. 

280.  If  the  price  of  a  farm  of  160  A.  2  R.  20  P.  be  $7850.- 
25,  what  will  be  the  price  of  another  farm,  containing  120  A. 
30  P.,  if  3  acres  of  the  latter  be  worth  4  of  the  former  1 

281.  A  man  bought  840  bushels  of  oats  in  New  York  at 
$.35  per  bushel,  and  sold  them  in  Connecticut  for  $349.44. 
The  transactions  being  made  by  weight,  how  much  advance 
upon  the  cost  was  the  selling  price  per  bushel  ? 

282.  A  gentleman,  traveling  east  from  Lawrenoe,  Kansas, 
in  95°  10'  W.  Long,  found,  on  arriving  at  Boston,  that  his 
watch,  an  excellent  time-keeper,  was  1  h.  36  min.  28  sec. 
slower  than  the  time  at  Boston.  What  is  the  longitude  of 
Boston  ? 

283.  The  revenue  of  the  English  Government  for  the  year 
1861  was  $332142625,  and  the  expenditures  for  the  same 
year  exceeded  the  revenue  by  3|^.  How  much  was  the 
national  debt  increased  during  the  year  1 

284.  A  and  B  can  do  a  work  in  lOjf  days  ;  B  and  C  in 
13^  days;  and  A  and  C  in  12  days.  In  what  time  would 
each  do  the  work  alone  1  and  how  long  would  it  take  them, 
working  all  together,  to  do  it  1 

285.  The  net  proceeds  of  a  shipmetit  of  hay,  sold  at  $14 
per  ton,  after  deducting  a  commission  of  S^,  and  $500  for 
other  charges,  were  $6290.  How  many  tons  of  hay  were 
shipped  1 


144  ARITHMETICAL    EXAMPLES. 

286.  Ill  how  many  years  is  a  day  gained  by  the  Gregorian 
Calendar,  which  allows  for  the  fraction  of  a  day  by  adding  97 
days  in  400  years  ? 

287.  How  many  shares  of  $50  each  must  be  bought  at  2b% 
discount,  brokerage  1|^,  and  sold  at  16^  discount,  brokerage 
11%,  to  gain  $134? 

288.  Boi^s  at  26^  premium,  brokerage  |^  cost  $527.93 
more  than  the  face ;  what  is  the  face  1 

289.  In  the  United  Kingdom  of  Great  Britain  593284200 
letters  were  delivered  in  the  year  1861,  of  which  4S6679200 
belonged  to  England  and  Wales,  or  24  to  each  inhabitant; 
50049000  belonged  to  Ireland,  or  9  to  each  inhabitant ;  and 
56556000  to  Scotland,  or  18  to  each  inhabitant.  What  was 
the  population  of  the  United  Kingdom? 

290.  A  flictor  receives  $30056,  and  is  directed  to  purchase 
cotton  at  $289  per  bale ;  he  is  to  receive  4^  commission. 
How  many  bales  doss  he  buy  ? 

291.  B.  F.  Sears  bought  a  house  and  lot,  Apr.  1,  1863,  for 
W'hlch  he  agreed  to  pay  $2500  on  the  IGch  of  the  following 
Nov.,  and  $1800,  Apr.  1,  1864.  If  he  could  have  got  a  dis- 
count of  9fo  for  present  payment,  how  much  would  he  have 
gained  by  borrowing  the  sum  at  7^,  and  how  much  would  he 
have  borrowed  ? 

292.  Three  men  engaged  in  the  lumber  trade ;  A  furnished 
$4000,  and  B  $6000 ;  they  gained  $1680,  of  which  Cs  share 
was  $840.     Required  C's  stock  and  A's  and  B's  gain. 

293.  If  a  cistern  19A  ft.  long,  lOi  ft.  wide,  and  12  ft.  deep, 
hold  546  barrels,  how  many  barrels  will  a  cistern  contain 
that  is  18  ft.  long,  9  ft.  wide  and  15  ft.  deep  ? 

294.  A  speculator  gained  25^^  on  §  of  his  investment,  and 
lost  b%  on  the  remainder  ;  his  net  profits  were  $1140.  Had 
he  gained  2bfo  on  -?,  and  lost  5^  on  the  remainder,  what  would 
have  been  his  net  profits? 

595.  A  lady  bought  23  yards  of  sheeting  and  57^  yards  of 


ARITHMETICAL   EXAMPLES.  145 

calico  ;  she  paid  2J  cents  more  per  yard  for  the  sheeting  than 
for  the  calico,  and  the  entire  cost  of  the  calico  was  twice  as 
much  as  the  sheeting.    What  was  the  price  of  each  per  yard  ? 

296.  I  is  how  many  per  cent,  of  |  ? 

297.  The  national  debt  of  England,  Mar.  1,  1862,  was 
£805000000.  If  this  debt  were  paid  in  silver,  of  which 
there  are  3  oz.  7  pwt.  12  gr.  to  a  £,  how  long  a  train  of  cars, 
allowing  each  car  to  occupy  a  space  30  ft.  in  length,  and  to 
carry  10  short  tons,  would  be  required  to  carry  it  ? 

298.  One  pound  of  gold  is  equal  in  value  to  14.29  pounds 
of  silver.  If  the  above  debt  were  paid  in  gold,  how  long  a 
train  would  be  required  to  carry  it? 

299.  A  merchant  bought  a  quantity  of  butter  at  $24  per 
cwt.,  cash.  For  how  much  per  pound  must  he  sell  it  to  gain 
16%,  and  allow  S%  discount  for  cash? 

300.  If  a  stone  20  inches  long,  15  inches  broad,  and  8 
inches  thick,  weigh  217  pounds,  what  will  be  the  length, 
breadth  and  thickness  of  a  similar  stone  that  weighs  13888 
pounds  ? 

301.  Twenty-five  workmen  have  agreed  to  labor  12  hours 
a  day  for  24  days,  to  pay  an  advance  made  to  them  of  $900, 
but  having  lost  each  an  hour  per  day,  five  of  them  engage  to 
fulfill  the  agreement  by  working  12  days.  How  many  hours 
per  day  must  these  labor  ? 

302.  Says  B  to  C :  "  -J  of  my  money  is  equal  to  -|  of 
yours,  and  the  difference  between  your  money  and  mine  is 
$10."     What  sum  had  each  ? 

303.  What  is  the  amount  of  $872.50  for  3  yr.  6  mo.  18 
da.,  at  7^%  1 

304.  Four  men  hire  a  pasture  of  125  A.  48  P.  at  $1.75  per 
acre ;  A  puts  in  125,  B  150,  C  200  and  D  225  sheep.  How 
much  rent  ought  each  to  pay  1 

305.  Sept.  15,  1862,  11460  men,  forming  12  regiments  of 
infantry  and  6  batteries,  surrendered  at  Harper's  Ferry  ;  the 

7 


146 


ARITHMETICAL    EXAMPLES. 


average  number  of  men  attached  to  each  battery  was  ^J  of 
the  average  number  in  each  regiment ;  there  were  123  pris- 
oners unclassified.  Required  the  number  of  infantry  and  ar- 
tillery and  the  total  surrender. 

30G.  Gave  |533.33|  of  notes  at  4fo  discount  for  .$500  gold. 
What  rate  of  premium  was  the  gold  ? 

307.  A  and  B  made  a  joint  stock  of  $1666,  and  gained 
1204,  of  which  B  had  $60  more  than  A.  How  much  did  each 
contribute  to  the  stock  '? 

308.  A  grocer  bought  11  bushels  of  chestnuts  at  $3.00  a 
bushel,  and  retailed  them  at  3  cents  a  half  pint.  What  ^ 
profit  was  his  gain  1 

809.  July  1,  1859,  four  balloonists  left  St.  Louis  at  4  h.  30 
min.  P.  M.,  and  landed  in  Jefferson  Co.,  N.  Y.,  1150  miles 
from  St.  Louis,  at  20  minutes  past  noon  of  July  2nd.  What 
was  the  average  velocity  per  minute  1 

310.  If  the  use  of  $6919.32  for  7  yr.  6  mo.  is  worth 
$3113.694,  what  sum  is  that  .whose  use  for  10  yr.  10  mo.  20  d. 
is  worth  $3266.66^  ? 

311.  Forty  per  cent,  of  brandy  is  alcohol.  How  much 
alcohol  does  a  man  drink  in  52  years,  if  he  take  |  of  a  gill 
of  brandy  3  times  a  day  1 

312.  A  house  that  rents  for  $848.25  cost  $8700.  What  fo 
does  it  pay  on  the  investaient  ? 

313.  When  shall  a  note  be  made  payable  to  balance  the 
following  account  ? 

James  Tyler. 


Dr. 


Cr. 


1860. 
June  12 
20 
30 
5 
16 
2d 


July 


To  Mdse.  on  3  mo. 


530  1.84 
2.-56  |4S 
739  56 
273  Ai 
194  1 78 
536  '42 


Sept. 
Oct. 


Not. 


14 

By  Cash, 

436 

OO 

'2b 

.320 

00 

ii 

560 

00 

17 

370 

00 

16 

840 

00 

24 

560 

00 

■314.  M,  N,  nnd  S,  are  partners.      On    closing   business, 
they  have  the  following  resources  and  liabilities;    cash  on 


ARITHMETICAL   EXAMPLES.  147 

hand,  ^5430 ;  shop  and  fixtures  valued  at  82500 ;  bills 
receivable,  $956 ;  Barns  &  Co.  owe  them  $8G5  ;  ten  shares 
in  Canal  R.  R.  stock,  $1000.  They  owe  on  notes  unre- 
deemed, $1865.  M  invested  $2400 ;  N,  83000,  and  S,  82700. 
What  is  the  net  gain  1 

315.  What  per  cent,  of  an  acre  is  2  R.  20  P.  1 

316.  In  the  battle  of  Perryville,  Ky.,  Oct.  8,  1862,  the 
Rebel  loss  in  killed  and  prisoners  together  was  50^^  of  the 
loss  in  wounded,  and  the  prisoners  were  ^^  of  the  killed' 
What  per  cent,  of  the  loss  were  prisoners  ?  The  prisoners 
numbered  200.     What  was  the  whole  Rebel  loss  ? 

317.  The  Federal  loss  in  the  same  battle  was  350  more 
than  I  the  rebel  lossj  the  prisoners  were  16^^  of  the  entire  loss ; 
and  the  killed  50  more  than  20,^^  of  the  entire  Federal  loss ; 
the  remainder  being  wounded,  what  was  their  number  1 

318.  At  $11.75  per  cwt.,  how  much  sugar  can  be  bought 
for  $90.25  ? 

319.  If  it  require  2250  bricks,  8  in.  long  by  4  in.  wide,  to 
pave  a  court  25  ft.  by  20  ft.,  how  many  tiles,  10  in.  long  by 
5  in.  wide,  will  be  required  to  pave  a  \valk  300  ft.  by  8  ft.  1 

320.  My  salary  is  $800  a  year.  If  I  pay  25^^:^  for  board, 
10^^  of  the  remainder  for  rent,  20,^  of  the  residue  for  clothes, 
$32  for  books,  and  loan  A  the  remainder,  what  fo  of  my  salary 
is  unexpended  ? 

321.  Invested  $3432  in  Government  bonds  at  106,^,  paying 
1-}^  brokerage,  and  afterward  sold  the  stock  at  12^^  pre- 
mium, brokerage  l^^L     What  was  my  gain  1 

322.  A  merchant  bought  a  quantity  of  flour  at  $8.00  per 
barrel  on  a  credit  of  3  months,  and  kept  it  6  months  ;  then 
sold  it  on  3  months'  credit,  and  gained  5fc.  Money  being 
worth  Q^,  for  how  much  did  he  sell  the  flour  per  barrel  ? 

323.  1  qt.  1|  pt.  is  what  per  cent,  of  2  gal.  3i  qt.  ? 

324.  I  own  $12500  in  a  Mutual  Lisurance  Company.    How 


148  ARITHMETICAL    EXAMPLES. 

many  shares  shall  I  possess  after  a  dividend  of  8^  has  been 
declared,  payable  in  stock  1 

325.  Twelve  million  gallons  of  petroleum  were  sent  to 
Europe  from  the  United  States  in  18G2  for  $3600000 ;  the 
cost  of  production  being  $.20  a  gallon,  what  was  the  rate  of 
profit  1 

326.  What  is  the  value  of  40  casks  of  sugar,  each  weigh- 
ing 12  cwt.  3  qr.  5  lb.,  draft  5^,  tare  10 fc,  at  $8.75  per  cwt. 
net? 

327.  At  what  rate  of  discount  must  the  Illinois  State  G'^ 
bonds  be  purchased  that  the  person  investing  may  receive  63^ 
upon  his  money  ? 

328.  Jones,  Brown,  Hall  &  Smith  are  partners;  Jones 
takes  I  of  the  gains  or  losses ;  Brown  |,  Hall  i,  and  Smith 
the  remainder.  At  the  close  of  the  year  the  resources  of  the 
firm  are :  Cash  $6875,  Merchandise  $8965,  Bonds  and  Mort- 
gages $7650,  Bank  Stock  $3000 ;  Jones  has  drawn  from  the 
business  $600,  Brown  $350,  and  Hall  $190;  the  liabilities 
are:  Notes  outstanding  $3640;  Balance  in  favor  of  Reed  &  Co., 
$750;  Balance  in  favor  of  Suffolk,  $2645 ;  Jones  invested 
$6365,  Brown  $5270,  Hall  $4180,  and  Smith  $2320.  What 
is  each  partner's  interest  in  the  business  at  the  close  of  the 
year  % 

329.  What  will  be  the  duty  at  Ahfo  on  a  case  of  jewelry 
and  watches  amounting  to  $2780  ? 

330.  A  merchant  bought  16  barrels  of  salt  at  $1|  per 
barrel,  and  put  it  into  sacks  of  10  and  25  lb.,  each  an  equal 
number,  selling  them  for  $.08  and  $.20  each.  What  ^fo  was 
his  profit  ? 

331.  In  the  series  of  battles  from  Aug.  27  to  Sept.  1,  1862, 
fought  before  Washington,  the  killed  of  the  Union  army  were 
50^  of  the  prisoners,  and  the  prisoners  33i^  of  the  wounded. 
What  per  cent,  of  the  wounded,  and  what  per  cent,  of  the 
whole  loss  were  the  killed  ? 


ARITHMETICAL    EXAMPLES.  149 

332.  The  total  Union  loss  in  the  above-mentioned  battles 
being  9000  ;  how  many  were  killed,  wounded,  and  taken  pris- 
oners, respectively  ? 

333.  Where  $37.70 f^  will  purchase  7  yd.  3|  qr.  of  cloth, 
what  is  the  price  per  yard  1 

334.  If  a  horse  trot  2  miles  in  5  min.  55  sec,  how  far 
would  he  trot  in  an  hour  at  the  same  rate  ? 

335.  A  ship  has  a  leak  that  will  fill  and  sink  her  in  24 
hours ;  all  her  pumps  are  capable  of  emptying  her  in  25  hours. 
If  the  pumps  are  worked  after  the  vessel  has  been  leaking  3 
hours,  how  long  before  the  ship  will  sink  1 

336.  How  much  wine  can  be  bought  for  $1.82,  when  a 
hogshead  is  worth  $70.56 1 

337.  Three  shafts  together  make  465  revolutions  in  a 
minute ;  the  first  makes  a  certain  number,  the  second  3  times 
as  many,  and  10  more,  and  the  third  15  less  than  twice  as 
many  as  the  second.  How  many  revolutions  does  each 
make? 

338.  A  farmer  sold  at  one  time  35  bushels  of  corn  and  60 
bushels  of  wheat  for  $157.50  ;  at  another  time  56  bushels  of 
corn  and  42  bushels  of  wheat  for  the  same  sum  of  money. 
What  was  the  price  of  each  per  bushel  ? 

339.  A  hired  a  house  for  one  year  for  $500 ;  at  the  end  of 
three  months  he  takes  in  H ;  and  after  3  months  more,  M ; 
and  at  the  end  of  9  months,  K.  At  the  end  of  the  year  how 
much  rent  must  each  pay  1 

340.  The  longitude  of  Paris  is  2°  20'  22"  E.,  and  of  Con, 
stantinople,  S°  59'  E.  When  it  is  1  A.  M.  at  the  latter  place, 
what  time  is  it  at  the  former  1 

341.  How  much  gold  at  QS^^^  premium  can  be  bought  for 
$5396  currency  ? 

342.  If  12  pipes,  each  delivering  12  gal.  a  minute,  fill  a 
cistern  in  3  h.  24  min.,  how  many  pipes,  each  delivering  16 


150  ARITHMETICAL   EXAMPLES. 

gal.  a  minute,  will  fill  a  cistern  6  times  as  large  in  G  hours 
48  minutes  1 

343.  The  earnings  of  the  Hudson  River  R.  R.  for  Feb. 
1864  were  $472240,  which  was  an  increase  of  11  i^  over  the 
earnings  for  the  same  month  in  1863.  How  much  was  the 
increase  1 

344.  A  town,  6  miles  square,  is  divided  into  325  equal 
farms.  What  must  A.  G,  Dickey  pay  for  one  of  these  farms 
at  121.25  per  acre  1 

345.  If  $1500  in  7  mo.  20  da.  produce  $95,833,  what  prin. 
cipal  must  be  loaned  to  gain  $53  in  10  mo.  26  da.  ? 

346.  M  and  N  enter  into  a  partnership  for  2  years ;  M 
puts  in  $8000,  and  N  $2500 ;  N  is  to  do  the  business,  and 
his  services  are  regarded  as  worth  the  use  of  $5500 ;  after  6 
months  M  increases  his  stock  to  $12000 ;  at  the  end  of  2 
years  the  partnership  is  closed,  and  there  is  a  net  gain  of 
$4750.     Required  each  partner's  share  of  the  gain. 

347.  A  merchant  bought  500  barrels  of  flour  at  $5.00  a 
barrel,  payable  in  3  months  ;  after  keeping  it  30  days,  he 
sold  it  for  $5.50  a  barrel,  receiving  a  note  payable  in  3 
months ;  the  purchase  money  becoming  due,  he  got  the  note 
discounted  at  a  bank  to  meet  it.  How  much  did  he  gain  by 
the  transaction  ? 

348.  "What  was  the  cost  of  12  Ohio  State  Bonds  of  $500 
each  at  12^  premium,  |^  brokerage  ? 

349.  At  the  battle  of  Pea  Ridge,  March  7,  1862,  j%  of  the 
whole  loss  of  the  Rebel  army  were  prisoners  ;  the  killed  were 
500  less  than  the  prisoners,  and  the  wounded  were  300  more 
than  twice  the  killed.     What  was  the  total  Rebel  loss  ? 

350.  If  a  man,  by  traveling  9  hours  each  day,  can  go  234 
miles  in  15  days  how  for  can  he  travel  in  30  days  of  8  hours 
each? 

351.  How  many  shares   of  mining  stock  at  80;^  must  be 


ARITHMETICAL    EXAMPLES.  151 

sold  ill  order  that  the  proceeds    invested  in  California  8's  at 
108^  may  yield  a  profit  of  $960  ? 

352.  The  duty  on  1000  drums  of  figs,  each  containing  14 
lb,,  invoiced  at  6|  cents  per  pound,  was  $74.37-^.  What  was 
the  rate  of  duty  ? 

353.  How  much  was  the  New  England  currency  depre- 
ciated at  the  adoption  of  United  States  money,  when  £1  was 
worth  $4i  ? 

354.  How  much  had  New  York  currency  depreciated  at 
the  same  time  ? 

355.  How  much  had  New  York  currency  depreciated 
below  New  England  ? 

356.  Sold  goods  to  a  certain  amount  on  a  commission  of 
5^,  and  having  remitted  the  net  proceeds  to  the  owner,  re- 
ceived for  prompt  payment  |^  which  amounted  to  $16.15. 
What  was  the  amount  of  commission  ? 

357.  What  is  the  difference  in  cost  between  a  draft  on 
Boston  of  $17302.80,  at  1|^  premium,  and  one  on  Chicago, 
for  the  same  amount,  at  ^^  discount  ] 

358.  A  man,  engaging  in  trade  with  $9600,  found  at  the 
end  of  3  years  that  he  had  gained  $138.75  more  than  -|  of  his 
capital.     What  was  his  average  annual  gain '? 

359.  In  1837,  the  silver  dollar  contained  412^-  grains  of 
standard  silver,  but  in  1853  the  weight  was  changed  to  384 
grains.  The  fineness  remaining  the  same,  one  dollar  of  the 
old  coinage  was  worth  how  much  of  the  new  1 

360.  A  man  has  a  piece  of  land  95|  rods  long  and  58i 
rods  wide,  which  he  wishes  to  lay  out  in  the  largest  possible 
square  lots  of  equal  size.     How  many  lots  will  there  be  1 

361.  A  owes  $1500,  of  which  $400  is  to  be  paid  in  4 
months,  $500  in  5  months,  and  $600  in  6  months.  If  he  pays 
the  whole  at  once,  at  what  time  must  he  make  the  payment] 

362.  What  is  the  duty  at  25^  on  27  tons  8  cwt.  3  qr.  20 
lb.  of  iron,  invoiced  at  $48  per  ton  ] 


152  ARITHMETICAL   EXAMPLES. 

363.  S.  r.  Root  has  cloth  at  13.50  per  yard,  and  S.  Smith 
has  hay  at  $14.70  per  ton.  If  in  trading  Root  puts  his  cloth 
at  $4.50,  what  should  Smith  charge  for  his  hay  1 

364.  The  Erie  Railroad  earned  from  all  sources,  during 
the  year  1863,  $10469480,  and  the  expenses  of  operating  the 
road  were  61^  of  the  earnings.  It  paid  for  interest,  rent  of 
other  roads,  taxes  and  sinking  fund,  $1986315.  July  1,  1863, 
it  paid  a  4^'%  dividend  upon  its  paid-in  capital  of  $14000000, 
and  a  5%  dividend  upon  the  same,  Jan.  1,  1864.  There  was  a 
surplus  of  $26621.28,  Jan.  1,  1863.  What  was  the  balance 
to  the  credit  of  the  road,  Jan.  1,  1864  ? 

365.  The  cargo  of  a  ship  is  worth  $96000,  and  4  of  i  of  j^^ 
of  the  cargo  is  worth  |  of  f  of  |  of  the  value  of  the  ship. 
What  is  the  value  of  the  ship  1 

366.  A  Boston  merchant,  having  received  an  importation 
of  wine  from  Lisbon,  invoiced  at  3008  milrees,  470  reis,  al- 
lows his  correspondent  in  Lisbon  to  draw  on  him  for  the 
necessary  sum,  exchange  on  the  United  States  being  in  Lis- 
bon 040  reis=$l.  How  much  would  the  merchant  have 
saved  by  remitting  a  draft  on  Lisbon  purchased  at  $1,055  per 
milree  ? 

367.  How  many  eagles,  each  containing  9  pwt.  16.2  gr.  of 
pure  gold  can  I  get  for  2278.269  oz.  pure  gold  at  the  mint, 
allowing  1^%  foi*  coining  expenses'? 

368.  A  "owes  B  $500,  payable  in  4  months ;  at  the  close  of 
2  months  he  wishes  to  make  such  a  payment  as  will  extend 
the  time  of  the  balance  to  one  year.  What  must  be  the  pay- 
ment? 

369.  Massachusetts  paid  $2750  internal  revenue  tax,  in 
1863,  on  gold  plate,  at  the  rate  of  $.50  per  ounce  Troy. 
What  was  the  value  of  the  gold  plate,  allowing  it  to  average 
18  carats  fine,  an  ounce  of  pure  gold  being  worth  $20,672  ] 

370.  A,  M  and  S  form  a  partnership,  with  capitals  of 
$5000,  $10000  and  $15000,  respectively  ;  A  draws  out  $500 


ARITHMETICAL    EXAMPLES.  153 

at  the  end  of  each  year,  M,  $800,  and  S,  $900 ;  at  the  end 
of  5  years  their  johit  capital  is  828600.  How  much  of  it 
does  each  own  ? 

371.  An  agent  received  $65  for  collecting  a  debt  of  $1800. 
What  was  the  rate  of  his  commission  ? 

372.  If  6  A.  3  R.  3  rd.  of  land  are  worth  £05  4s.  9d.,  what 
is  the  value  of  47  A.  1  R.  21  rd.,  U.  States  money,  sterling 
money  being  10|^  above  the  par  value? 

373.  If  the  net  earnings  of  a  bank  with  $250000  capital 
are  enough  to  pay  an  annual  dividend  of  10^,  and  reserve  a 
surplus  of  $2500,  also  to  pay  8^5^  of  its  net  earnings  to  the 
State  instead  of  taxes,  what  is  the  rate  of  taxation  on  its  cap- 
ital ? 

374.  The  Lackawanna  and  Bloomsburg  Railroad  paid 
$254384  expenses  for  one  year,  and  $141985  interest,  leaving 
a  surplus  equal  to  Sffj%  of  the  capital  stock  of  $1342500. 
What  were  the  gross  earnings  for  the  year? 

375.  A's  gain  was  $840,  B's  $1125,  C's  $1820;  A's  capi- 
tal was  in  trade  7  months,  B's  9  months,  and  C's  1  yr.  2 
months.     How  much  of  the  capital,  $13875,  did  each  own  ? 

376.  A  merchant  marked  a  piece  of  goods  25;^  above  the 
cost,  but  its  season  passing,  he  determined  to  sell  it  20^  be- 
low the  marked  price,  supposing  he  should  make  b</o.  Did 
he  make  or  lose  1 

377.  Exchanged  156  bu.  3  pl^.  7  qt.  1  pt.  of  wheat,  at  $.93| 
per  bushel,  for  87A  yd,  of  silk  at  $  87 A  per  yard,  and  the 
balance  in  cash.     How  much  money  was  received  ? 

378.  James  Fitch  owes  three  notes  to  George  Holmes ; 
one  of  $200,  due  in  8  months;  another  of  $200,  due  in  16 
months ;  and  the  third  of  $400,  due  in  2  year.-;.  Should  the 
three  notes  be  converted  into  two  notes  of  equal  amount,  one 
to  run  one-half  as  long  as  the  other,  when  ought  they  to  be 
made  payable? 

379.  The  cost  of  constructing  all  the  canals  in  New  York, 


154  ARITHMETICAL    EXAMPLES. 

up  to  1802,  was  $02292500 ;  the  amount  of  tolls  collected 
from  these,  in  1801,  was  $3908785.  How  much  less  were 
the  tolls  than  the  legal  interest  upon  the  sum  invested  in 
building  the  canals  ? 

380.  1  of  a  quarter  is  what  per  cent,  of  |  of  a  cwt.  ? 

381.  The  sales  of  a  clothing  house  amount  to  $100000  a 
year ;  |.  of  the  sales  are  made  at  a  profit  of  25^,  ^^  at  a  profit 
of  20^,  and  the  remainder  at  a  loss  of  4^.  Required  the 
cost  of  the  goods. 

382.  A  company  of  50  men  drank  wine  at  2s.  6d.  per  bot- 
tle, to  the  amount  of  £10.  How  many  men  at  the  same  rate 
will  £18  worth  of  wine  supply,  when  wine  is  worth  2s.  3d.  per 
bottle  ? 

383.  What  must  be  paid  in  Philadelphia  for  a  draft  on  St. 
Louis,  drawn  at  90  days,  for  $5000,  at  a  premium  of  1|^? 

384.  A  merchant  in  Cincinnati  wishes  to  remit  $14331.60 
to  New  York.  Exchange  on  New  York  is  ^^  premium,  but 
on  St.  Louis  A^  premium,  from  St.  Louis  to  New  Orleans 
l^  discount,  and  from  New  Orleans  to  New  York  1^  dis- 
count. What  will  be  the  value  in  New  York  by  each  method, 
and  how  much  better  is  the  circular  ? 

385.  The  gross  earnings  of  the  Erie  Railroad  for  1861 
were  $5590916,  and  the  expenses  were  $4067391.39  ;  the 
gross  earnings  of  the  same  road  for  1863  were  $10469480, 
and  the  expenses  $6386382.80.  How  much  greater  ^  were 
the  net  earnings  of  the  gross  earnings  in  1863  than  in  1861  ? 

386.  What  is  20,^  of  30^^  of  50,^  of  $66.6632  ? 

387.  A  man  can  sell  his  firm  for  $4000  cash,  or  for  $5000, 
payable  in  2  years.  If  he  accept  the  last  offer,  and  receive 
instead  its  present  worth,  at  10 fo  discount,  how  much  more 
would  he  receive  than  by  the  former  1 

388.  If  he  accept  the  first  offer,  and  loan  the  $4000  at  10^^ 
interest,  how  much  less  would  he  receive  at  the  end  of  2  years 
than  bv  the  second  offer  ? 


ARITHMETICAL   EXAMPLES.  155 

389.  "What  is  the  interest  of  8193.G8  from  Nov.  27,  1859, 
to  July  3,  186->,  at  l^fcl 

390.  AYlien  $2.57  are  paid  for  8  gal.  1  pt.  of  milk,  what 
is  the  price  per  quart  ? 

391.  The  manufacturers  of  Massachusetts  paid  in  one  year 
$3251325  internal  revenue,  which  was  23j^q  per  cent,  of  the 
sum  paid  by  all  the  manufacturers  in  the  United  States.  Re- 
quired the  entire  revenue  from  this  source. 

392.  If  I  gain  $46.27  on  8578.37^  worth  of  sugar,  how 
many  dollars'  worth  must  I  sell  to  gain  $134.64? 

393.  A  man  obtained  an  insurance  for  life  at  the  age  of  37, 
and  died  when  51  years  old.  The  policy  required  annual 
payments  during  life,  at  82.8674  per  $100,  and  secured  to  the 
heirs  $1709.69  more  than  the  amount  of  all  the  premiums 
paid.     What  was  the  face  of  the  policy  ? 


394.  $3250.  Hartford,  March  6,  1859. 
On  demand  we  promise  to  pay  Brown  &  Gross,  or  order, 

three  thousand  two  hundred  and  fifty  dollars,  for  value  re- 
ceived. 

Church  &  Brothers. 

Indorsed  as  fallows:  July  1,1859,  $406.87-];  Nov.  7, 
1859,  $50;  Jan  1,  1860,  $285  ;  Aug.  10,  1860,  $400.62; 
July  1,  1861,  $125;  Nov.  4,  1862,  $544.60;  Apr.  22,  1863, 
$4T3.76 ;  July  1,  1863,  $600.     What  was  due  Apr.  1,  1864  ? 

395.  A  grocer  bought  760  lb.  of  Java  coffee,  at  26  cents 
per  pound.  Allowing  16;^  for  shrinkage  in  roasting  and 
grinding,  at  what  price  per  pound  must  he  sell  it  to  gain  2d^  1 

396.  If  it  require  50.000  bricks  to  build  a  house  whose 
walls  are  1  ft.  6  in.  thick,  20  ft.  high,  and  108  ft.  long,  how 
many  will  build  one  whose  walls  are  2  ft.  thick,  30  ft.  high, 
and  324  ft.  long  ? 

397.  A  man  33  years  old,  takes  out  a  policy  for  $2000,  the 
payments  to  cease  at  50,  the  annual  premium  being  $3.50  per 


156  ARITHMETICAL    EXAMPLES. 

$100.     If  he  survive  that  age,  how  much  more  money  will  he 
receive  from  the  company  than  he  pays  them  1 

398.  In  the  year  1860,  6Q^%  of  all  the  printing  in  the  New 
England  States  was  done  in  Massachusetts ;  14'^^  in  Connecti- 
cut; 61%  in  Maine;  2fg%  in  Vermont;  Rhode  Island  per- 
formed ^J  as  much  as  New  Hampshire;  the  cost  of  the  print- 
ing done  in  Rhode  Island  was  1107360  more  than  the  cost  of 
what  was  done  in  Vermont.  Required  the  value  of  all  the 
printing  done  in  the  New  England  States  for  the  year  1860. 

399.  Paid  $5392.35  in  New  York  for  a  30  days'  draft  on 
Boston,  exchange  being  at  ?j^  premium.  Required  the  face 
of  the  draft. 

400.  Smith  &  Boise  traded  in  company  with  a  joint  stock 
of  18400.  Smith's  money  was  invested  14  months,  and  Boise 
10  months.  The  profits  being  equally  divided,  how  much  of 
the  capital  did  each  furnish  ? 

401.  A  man  with  the  proceeds  of  a  note  for  $4164.22  on 
60  days,  discounted  at  6^,  purchased  flour  at  $10.25  per  bar- 
rel, allowing  i^  commission  to  a  factor  for^buying  it.  At  the 
end  of  1  month  he  sold  the  flour  on  90  days'  credit  for  $11.50 
per  barrel ;  when  his  note  at  the  bank  matured,  he  had  the 
note  received  for  the  flour  discounted,  and  paid  his  own  note. 
How  much  did  he  gain  by  the  transaction  1 

402.  If  4  gal.  1  qt.  1  pt.  of  oil  is  bought  for  $1,235,  what  is 
the  price  per  gallon  1  • 

403.  The  total  sales  of  Wheeler  &  Wilson's  sewing  ma- 
chines for  seven  years  ending  Jan.  1,  1860,  were  38991 ;  of 
Grover  &  Baker's,  24818  ;  of  Singer's,  23353,  and  of  all  others 
such  a  number  that  the  aggregate  sales  of  all  kinds  were 
103372.  What  was  the  value  of  the  miscellaneous  class  at  an 
average  price  of  $30  a  machine  ? 

404.  A  farmer  had  a  dairy  of  48  cows,  each  furnishing  18 
qt.  of  milk  a  day,  from  which  he  made  40  cheeses  of  60  lb. 
each  in  30  days.  He  made  a  contract  to  deliver  100  cheeses 
of  96  pounds  each  in  80  days.     How  many  cows  must  he 


ARITHMETICAL    EXAMPLES.  157 

add  to  his   dairy  provided    each   additional    cow  furnish  4 
gallons  of  milk  daily  ? 

405.  In  what  time  will  $3045.20  gain  $190.32  if  the  gain 
of  $2494.75  for  1  yr.  13  d.,  is  $258.48,  and  what  is  the  rate 
per  annum  1 

406.  Marks,  Willis  &  Sterrett  were  partners  in  the  flour- 
ing business ;  Marks  had  invested  ^,  Willis  i,  and  Sterrett  /^ 
of  the  capital.  They  were  to  share  equally  the  gains  or  losses. 
The  business  not  being  successful,  the  partnership  was  dis- 
solved at  the  close  of  the  year,  when  the  resources  of  the  firm 
were  found  to  be :  Cash,  $1785 ;  wheat  on  hand,  $2500 ;  corn, 
$1752;  rye,  $350;  flour,  $1050;  mill  and  fixtures,  $5000. 
The  liabilities  were:  Notes  outstanding,  $1562;  they  owed 
Milo  Chidsey,  $1200,  and  S.  Combs,  $1875.  The  net  losses 
were  $750.  What  was  the  net  capital  of  the  firm  at  com- 
mencing, and  what  was  each  partner's  net  capital '? 

407.  What  is  the  distance  around  a  rectangular  field,  whose 
length  is  twice  its  breadth,  if  one  end  measures  35  rd.  5  yd. 
2  ft.  6  in.  1 

408.  The  average  number  of  horse  cars  running  daily  on 
the  railroads  of  Boston  and  vicinity,  is  132 ;  and  each  car 
carries  an  average  of  2000  passengers  per  week  ;  the  average 
fare  being  4d.  N.  E.  currency,  what  is  the  net  income  of  all 
the  roads  per  year,  the  expense  of  working  the  roads  being 
$624936,  supposing  1000  passengers  do  not  pay  fare"? 

409.  When  exchange  at  New  York  on  Paris  is  5  francs  25 
centimes  per  $1,  and  at  Paris  on  Hamburg  2j-  francs  per 
mark  banco,  what  will  be  the  arbitrated  price  in  New  York 
of  6580  mark  bancos  ? 

410.  The  value  of  real  estate  and  personal  property  in  the 
United  States  in  1860  was  $16159616068;  the  debt  of  the 
United  States  Jan.  1,  1864,  was  $1373567365.78  ;  if  a  direct 
tax  were  levied  to  cancel  the  debt,  what  would  be  the  rate  of 
taxation,  and  how  much  would  John  Smith  pay  who  is  worth 
85000? 


158  ARITHMETICAL   EXAMPLES. 

411.  How  many  bushels  of  corn  in  Illinois  are  equal  to 
SOOO  bushels  in  New  York  ? 

412.  What  is  the  value  of  a  house  and  lot  that  pays  a 
profit  of  9  per  cent,  by  renting  it  at  $50  per  month  ? 

413.  A  draft  was  purchased  in  New  York  on  Chicago  for 
$3000,  drawn  at  60  days,  for  |2850.  What  was  the  course 
of  exchange  ? 

414.  How  many  bushels  of  oats  in  Connecticut  are  equal 
to  5000  bushels  in  Iowa  ? 

415.  A  farmer  sold  three  hogs,  one  weighing  275  pounds, 
at  5  cents  per  pound;  a  second,  weighing  310  pounds,  at  5 A 
cents  per  pound ;  and  the  third,  weighing  345  pounds,  for 
$25.     What  was  the  average  price  per  pound  for  the  whole? 

416.  At  what  rate  of  premium  is  Prussian  coin,  when 
$352.92  in  United  States  silver  coinage  of  1837,  is  paid  for 
500  thalers  1 

417.  A  father  left  his  four  sons,  whose  ages  are  15,  11,  7 
and  6  years,  $57770,  to  be  so  divided  that  the  respective 
parts  placed  at  simple  interest  in  Connecticut  shall  amount  to 
equal  sums  when  they  become  21  years  of  age.  What  are 
these  parts  ? 

418.  It  is  estimated  that  a  sewing  machine  does  the  work 
of  six  persons,  and  that  its  use  in  making  boots  and  shoes  in 
Massachusetts  annually  saves  $7500000 ;  allowing  300  work- 
,ing  days  in  a  year,  and  $1.25  as  the  average  daily  wages 
of  shoemakers,  how  many  persons  engaged  in  this  trade  docs 
the  use  of  sewing  machines  leave  free  to  follow  other  pursuits  ? 

419.  A  grocer  sold  12  hams,  each  weighing  15  lb.,  at  12  J 
cents  per  pound,  and  took  in  payment  1  load  of  apples,  con- 
sisting of  18  bags,  each  containing  2\  bushels.  Kequired  the 
price  of  the  apples  per  bushel. 

420.  A  merchant  in  New  York  wishes  to  pay  £3000  in 
London.  Exchange  on  London  is  9  j,^  premium ;  on  Paris, 
5  francs  25  centimes  per  $1,  and  on  Amsterdam  40  cents  to 


ARITHMETICAL   EXAMPLES.  159 

a  guilder.  The  exchange  between  France  and  England  at  the 
same  time  is  25  francs  to  £1,  and  that  of  Amsterdam  on 
England  12i  guilders  to  £1.  Which  is  the  most  advanta- 
geous, the  direct  exchange,  or  through  Paris,  or  through 
Amsterdam "? 

421.  Received  from  Charleston  500  bales  of  cotton,  each 
weighing  560  lb.,  invoiced  at  9d.  per  lb.  Georgia  currency ; 
sold  it  at  an  advance  of  20 fc,  commission  life,  and  remitted 
the  net  proceeds  by  draft.  What  was  the  face  of  the  draft, 
exchange  being  l^f,  discount? 

422.  There  were  15S366425  bushels  of  bituminous  coal, 
and  9416333  tons  of  anthracite  coal  mined  in  the  U.  S.  in 
1860,  and  25  bushels  of  the  bituminous  made  one  ton ;  the 
average  cost  of  the  coal  at  the  mines  being  $1.30  per  ton,  what 
was  the  total  value  of  all  the  coal  mined  ?  The  value  in  1850 
being  $7173750,  what  was  the  rate  of  increase  in  ten  years'? 

423.  A  merchant  in  Syracuse,  N.  Y.,  purchased  a  draft  on 
Chicago  for  $2660,  drawn  at  60  days,  paying  $2570.89. 
What  was  the  course  of  exchange  1 

424.  A  horse  which  was  bought  for  20^^  less  than  his  real 
value,  became  injured,  and  was  sold  for  40fc  less  than  his 
cost,  at  a  price  $130  below  his  original  value.  For  how  much 
was  he  sold  ? 

425.  A  gentleman  sent  a  silver  cake  basket,  weighing  3 
pounds  9  ounces,  to  a  jeweler,  and  ordered  him  to  take  SJ;:^ 
of  it  for  his  work,  and  manufacture  the  remainder  into  small 
dessert  spoons,  each  weighing  1  oz.  9  pwt.  How  many  dozen 
spoons  ought  he  to  receive  ? 

426.  I\Iy  agent  purchased  for  me  in  Liverpool  a  cargo  of 
iron  costing  £8500;  when  the  ship  arrived  in  New  York  I 
purchased  a  bill  on  Liverpool  for  the  amount,  exchange  being 
184;c ;  also  paid  ZOfo  duties,  gold  being  172^:,^.  For  how 
much  must  I  sell  the  cargo  to  gain  25^^  on  the  entire  cost, 
provided  I  have  U.  S.  currency  with  which  I  purchase  the 
bill  on  Liverpool,  and  the  gold  for  paying  the  duty  ? 


CHAPTEE  YI. 

1.  The  Winchester  bushel  is  of  cylindrical  form,  18.5  in. 
in  diameter,  and  8  in.  deep.  What  must  be  the  dimensions 
of  a  cubical  box  which  shall  contain  27  bushels  ? 

2.  A  gentleman  deposited  in  a  savings  bank  for  his  son,  15 
years  of  age,  a  sum  of  money,  which,  at  5^  compound  inter- 
est, payable  semi-annually,  amounted  to  $10000  at  his  major- 
ity.    What  was  the  sum  deposited  1 

3.  A  grocer  mixed  5  lbs.  of  sugar,  at  8|  cts.  per  pound, 
with  80  lbs.,  at  7|  cts.  per  pound,  and  60  lbs.  at  such  a  price 
that  the  mixture  was  worth  9|  cts.  per  pound.  Required 
the  price  per  pound  of  the  last  kind  of  sugar. 

4.  How  much  less  will  it  cost  to  fence  32  A.  64  P.  in  the  form 
of  a  circle,  than  in  the  form  of  a  square  1  and  how  much  less 
in  a  square  form  than  in  the  form  of  a  rectangle,  whose  length 
is  4  times  its  width,  the  price  in  each  case  being  $1.50  per 
rod? 

5.  One-third  of  a  quantity  of  goods  was  sold  to  gain  a 
certain  %,  one-fourth  to  gain  1^  times  as  much  ^,  and  the 
remainder  to  gain  2i  times  as  much  ^.  What  is  the  gain  % 
on  each  part,  the  gain  upon  the  whole  being  21^  ? 

6.  If  a  cask,  45  inches  long  and  36  inches  bung  diameter, 
contain  167  gallons  of  wine,  what  must  be  the  length  and 
bung  diameter  of  a  cask  of  the  same  shape,  containing  314 
gallons  ? 

7.  If  $600  gain  $72  in  1  yr.  6  mo.,  in  what  time  will  $850 
gain  $189.83J  1 


ARITHMETICAL    EXAMPLES.  161 

8.  Two  mechanics  work  together;  for  10  days' work  of  the 
first  and  8  days'  work  of  the  second  they  receive  $50 ;  and 
for  15  days'  work  of  the  first  and  14  days'  work  of  the  second 
they  received  681.     What  is  each  man's  daily  wages  ? 

9.  It  is  80  rods  between  the  opposite  corners  of  a  square 
field.     How  many  acres  in  the  field  ? 

10.  Four  towers— A  125  feet  high,  B  25  yards  high,  C  160 
feet  high,  and  D  70  feet  high — stand  upon  the  same  plane; 
B  directly  south,  and  40  rods  from  A  ;  C  east  from  B  ;  and 
D  south  from  C.  The  distance  from  A  to  C  plus  the  distance 
from  C  to  B  is  i  a  mile,  and  the  distance  from  D  to  B  is  82i 
yards  farther  than  the  distance  from  C  to  D.  Required  the 
length  of  a  line  to  connect  the  tops  of  A  and  D. 

11.  A  farmer  took  some  butter  to  the  store  and  received 
therefor  $12.25,  the  price  per  pound  being  as  many  cents  as 
there  were  pounds.     How  many  pounds  were  there  ? 

12.  A  miller  is  required  to  grind  160  bushels  of  provender, 
worth  $1.00  a  bushel,  from  oats  worth  $.40,  corn  worth  $.80, 
barley  worth  $.90,  and  rye  worth  $1.10,  and  wheat  worth 
$1.30  per  bushel.  How  many  bushels  of  each  kind  may  he 
take  ? 

13.  There  is  a  park  containing  15  A.  3  R.  30  P.,  and  the 
breadth  is  |  the  length.  If  two  men  start  from  the  same 
corner  and  travel  at  the  rate  of  4  miles  per  hour,  one  going 
around  the  park,  and  the  other  taking  the  diagonal,  how  much 
sooner  will  the  latter  reach  the  opposite  corner  than  the  for- 
mer? 

14.  If  I  own  I  of  a  farm,  and  sell  §  of  my  share  for  $3460, 
what  part  remains  to  me?  and  what  is  the  whole  farm 
worth  ?  ^ 

15.  G  and  H  trade  in  company;  G's  capital  is  |  of  H's : 
at  the  end  of  5  months  H  draws  out  ^  of  his  capital ;  and  at 
the  end  of  9  months  G  draws  out  4  of  his.  What  part  of  the 
gain,  which  is  $4222.50,  should  each  have  at  the  end  of  the 
year  ? 


162  ARITHMETICAL    EXAMPLES. 

16.  I  owe  a  man  the  following  notes:  one  of  |500,  due 
April  1 ;  one  of  $750,  due  July  15  ;  and  one  of  $1750,  due 
Sept.  10.  The  holder  wishes  to  exchange  them  for  two  notes 
of  11500  each,  and  wants  one  to  fall  due  May  10;  when 
should  the  other  be  made  payable  ? 

17.  A  and  B  traded  together;  A  put  in  $400  for  512  days, 
and  received  4  of  the  gain ;  the  number  of  dollars  which  B 
put  in  was  equal  to  the  number  of  days  it  was  employed  in 
trade.     What  was  B's  capital  ? 

18.  The  longitude  of  Springfield,  Mass.,  is  72°  35'  45"  W., 
and  of  Constantinople,  28°  49'  E.  When  it  is  9  o'clock  A.  M. 
at  the  latter  place,  what  time  is  it  at  the  former  ? 

19.  A  note  was  given  for  $500,  with  interest  payable  an- 
nually, at  Ifc.  Nothing  having  been  paid  for  10  years,  how 
much  did  the  total  amount  of  interest  due  exceed  the  simple 
interest  of  the  principal  ^ 

20.  A  rectangular  piece  of  land,  containing  8  A.  1  R.  32 
sq.  rd.  is  J  as  wide  as  it  is  long.  What  is  the  distance  around 
it? 

21.  Bought  a  quantity  of  goods  for  $2500  cash,  and  sold 
them  for  $3125  on  3  months'  credit.  What  did  I  gain,  money 
being  worth  ^fo  1 

22.  What  is  the  difference  between  the  interest  and  dis- 
count of  $730,  for  5  yr.  9  mo.,  at  8  per  cent.'? 

23.  Wishing  to  ascertain  the  height  of  a  tower,  1  erected 
near  it  a  stick  2]-  feet  high ;  by  measurement  I  found  the 
shadow  of  the  tower  to  be  36|  ft.,  and  of  the  stick  9  in. 
at  the  same  time.     Required  the  height  of  the  tower. 

24.  A  man  agreed  to  v/ork  for  a  blacksmith  for  $1.50  per 
day  and  his  board  ;  for  each  day  lost  he  was  to  allow  $.40. 
At  the  end  of  11  weeks  he  received  $77.15.  How  many 
days  did  he  lose  1 

25.  What  is  the  daily  interest  on  $63300  in  U.  S.  demand 
notes,  bearing  7/g^  interest  1 


ARITHMETICAL   EXAMPLES.  163 

26.  A  ship  sailed  due  south  and  due  east  on  alternate  days, 
at  the  same  rate  each  day ;  at  the  end  of  six  days  it  was  found 
to  be  203.646  miles  south-east  from  the  place  of  starting. 
What  was  the  daily  rate  of  sailing  ] 

27.  If  a  body  put  in  motion  move  |  of  an  inch  the  first 
second,  ^  an  inch  the  second,  1  inch  the  third,  and  so  continue 
to  increase  its  velocity  in  geometrical  ratio,  how  far  would  it 
move  in  f  of  a  minute  ? 

28.  An  importer  sold  cloth  to  a  wholesale  dealer  at  1 0% 
advance ;  the  wholesale  dealer  sold  it  to  a  clothier  at  12^^ 
advance ;  the  clothier  sold  it  at  a  farther  advance  of  25^,  and 
received  81452.     How  much  did  it  cost  the  importer  1 

29.  The  Federal  debt,  Feb.  16,  1864,  was  officially  stated 
to  be  $1482600000.  What  per  cent,  is  that  of  the  whole 
taxable  property  of  the  loyal  States,  the  latter  being  esti- 
mated at  $14000000000 1 

30.  What  is  the  balance  of  the  following  account,  and  when 
is  it  due  ? 

Thomas  Lardner. 

Dr.  Cr. 


1860.     I 
March  1     To  Sundries, 
April  12       "   Mdse. 
July   16      "      " 
Sept.  14  I    "      " 


436      00  I    March  25  '  By  Draft  at  CO  da.  I  400  I  00 

548      00  I     April     6  |    "       "  30  "     i  650  I  00 

312      00  j!  June    20      "   Cash,  200  |  00 

536  1  00  ll  Aug.      3  1"  84  i  00 


31.  When  shall  a  draft  for  the  settlement  of  the  following 
account  be  made  payable  ? 

David  Sanford. 


Dr. 

Cr. 

1859. 

II     1859. 
36    !  April  1 
45    1  May  16 
T5  I    June  12 

1          ] 

Jan.        1 

To  Mdse.  on  3  mo 

54 

By  Cash, 

50  i  00 

Feb.      12 

"      •'       "  2    " 

28 

"    Draft  at  30  da. 

1     30     00 

March  16 

"   Sundries 

95 

i  125    00 

June     25 

"   Mdse. 

26 

32,1     "      20 

"  Cash, 

1  150  ,  00 

32.  Three  contractors  engaged  to  build  a  piece  of  road  for 
$8775;  A  employed  20  hands  24  days,  10  hours  a  day  ;  B, 
25  hands  20  days,  12  hours  a  day ;  and  C,  30  hands  25  days, 
9  hours  a  day.     How  much  should  each  contractor  receive  ? 


164 


ARITHMETICAL   EXAMPLES. 


33.  A  quantity  of  wheat  was  heaped  up  in  a  corner  of  a 
square  room  forming  a  portion  of  a  cone,  of  which  the  per- 
pendicular height  was  4  ft.  3  in.  and  the  slant  height  7  ft.  1  in. 
What  was  its  value  at  $1.66-  a  bushel? 

34.  Oliver  Wainwright. 

Dr.  Cr. 


1853. 

1 

1858. 

Jan.        1 

To  Mdse. 

36 

72 

Jan.      10 

By  Cash, 

98 

72 

Feb.        1 

It      11 

48 

'25 

21 

"     " 

25 

84 

March  17 

n          « 

72 

36 

March  23 

"   Sundries, 

15 

17 

April      1 

(1       (( 

93 

48 

April      6 

"         " 

8 

96 

If  the  above  account  were  settled  April  6,  1858,  by  draft 
on  time,  how  many  days'  credit  should  be  given  ? 


35.  11200. 


CmcAGO,  Jan.  1,  1858. 


For  value  received,  I  promise  to  pay  Stephen  Hopkins,  or 
order,  twelve  hundred  dollars,  on  demand,  with  interest  at  7^. 

Thomas  Bobbins. 

Indorsed  as  follows:  Jan.  1,  1859,  $300;  March  16,  1860, 
1350;  Jan.  1,  1862,  $250.  What  was  due  February  20, 
1864? 

36.  A  church  is  80  fl.  long  and  50  ft.  wide,  and  the  eleva- 
tion of  the  roof  is  14  ft.;  the  rafters  extend 2 ft. beyond  the 
plates,  and  the  boarding  projects  2  ft.  at  each  end.  How 
many  feet  of  boards  will  be  required  to  cover  the  roof,  allow- 
ing I  for  waste  ? 

37.  Divide  j|  of  a  piece  of  cloth,  which  contains  45 1  yd., 
into  equal  parts,  each  of  which  shall  contain  3%  of  the  whole 
piece.     How  many  yards  in  each  part  ? 

38.  If  it  cost  $85.60  to  inclose  a  circular  field  containing 
2  A.  28  P.,  how  much  will  it  cost  to  inclose  another  con- 
taining 26  A.  23  P.? 

39.  A  merchant  in  New  York  gave  $1000  for  a  bill  on 
London  of  £200.     What  was  the  rate  of  exchange  ? 

40.  A  grocer  desires  to  mix  teas  worth  $1.50  and  $1.20, 
with  140  pounds  worth  $.75,  that  the  mixture  may  be  worth 
$1.00.     What  quantities  of  each  must  he  takel 


ARITHMETICAL    EXAMPLES.  165 

41.  A,  B  and  C  traded  in  company;  A  put  in  $1400;  B, 
12500,  and  C,  300  barrels  of  flour ;  they  gained  82300,  of 
which  C  took  $1000.  What  were  the  shares  of  A  and  B,  and 
what  was  the  price  of  C's  flour  per  barrel  ? 

42.  An  orchard  containing  6  A.  12  sq.  rd.  is  3  times  as 
long  as  it  is  wide.     Required  the  length  and  breadth. 

43.  If  from  68  and  82  respectively,  a  certain  number  be 
subtracted,  J  of  the  first  remainder  will  be  equal  to  ^  of  the 
last.     What  is  the  number  subtracted  1 

44.  A  man  left  $10000  to  be  divided  between  his  three 
sons,  whose  ages  were  10  yr.,  13  yr.  4  mo.,  17  yr.  6  mo.,  re- 
spectively, in  such  proportions  that  the  share  of  each  at  sim- 
ple interest  at  6^,  should  amount  to  the  same  sum  when  they 
should  arrive  at  the  age  of  21  years.  What  was  each  one's 
share  1 

45.  A  grocer  sells  a  farmer  150  lb.  of  sugar  at  14  cents  a 
pound  and  makes  5^;  the  farmer  sells  him  150  lb.  of  meat 
at  12  cents  a  pound,  and  makes  a  profit  of  8%.  W^hich  gains 
the  more  by  the  trade  and  how  much  1 

46.  A  mechanic  received  $3  a  day  for  his  labor,  and  paid 
$5  a  week  for  his  board ;  at  the  end  of  8  weeks  he  had  saved 
$74.     How  many  days  did  he  work  ? 

47.  The  great  pyramid  built  by  Cheops  has  a  square  base 
746  ft.  on  each  side,  and  its  perpendicular  hight  is  450  feet. 
What  is  the  area  of  the  base,  of  each  side,  and  how  many 
cubic  feet  of  masonry  does  it  contain  ? 

48.  A  trader  bought  merchandise  as  follows :  Apr.  8, 
$150.22;  May  23,  $55.64,  on  30  da.;  June  2,  $82.60  on  2 
mo.,  and  July  14,  $90.  What  was  due  on  the  account  Sept. 
26,  money  being  worth  7^  ? 

49.  A  plot  of  ground  is  80  rods  square.  ,  What  is  the 
breadth  of  a  graveled  walk  around  it,  covering  an  area 
equal  to  J  the  area  of  the  field  1 

50.  A  gentleman  bought  an  annuity  of  £500  ii)  English 


166  ARITHMETICAL    EXAMPLES. 

consols,  bearing  Sfo    interest  for  20  years.     What  was   the 
present  worth  1 

51.  An  importer  sold  a  quantity  of  goods  to  a  wholesale 
merchant  at  an  advance  of  10  ,^;  the  latter  sold  them  to  a  re- 
tailer, gaining  12.]^,  and  the  retail  merchant  sold  them  for 
83093.75,  gaining  thereby  25^^.  How  much  did  the  goods 
cost  the  importer  ? 

52.  There  are  three  houses  so  situated  that  the  lines  con- 
necting them  form  an  equilateral  triangle,  the  sides  of  which 
are  70  rods  in  length.  How  many  acres  are  included  in  the 
triangle  ? 

53.  A  merchant  failing  in  business  can  pay  76  cents  on  a 
dollar.  He  offers  to  pay  his  whole  indebtedness  without 
interest  in  five  years  if  his  creditors  will  allow  him  to  go  on 
with  his  business ;  his  offer  being  accepted,  how  much  will  his 
creditors  lose  in  the  five  years,  money  being  worth  7%  ? 

54.  In  how  many  different  positions  may  a  family  of  7 
persons  seat  themselves  at  a  table  ? 

55.  A  triangular  orchard  has  1  tree  in  the  first  row,  3  in 
the  second,  5  in  the  third,  and  so  on  in  arithmetical  progres- 
sion.   How  many  trees  in  the  orchard,  there  being  50  rows  1 

56.  What  are  the  interior  dimensions  of  a  cubical  box  that 
contains  40  bushels  of  grain  '? 

57.  How  many  strokes  of  a  common  clock  are  struck  in  24 
hours  ? 

58.  A  man  wishes  to  enclose  a  circular  field  which  shall 
contain  o'^-  as  many  acres  as  it  will  require  rails  to  build  a 
fence  around  it.  The  rails  being  15  feet  long,  and  the  fence  6 
rails  high,  how  many  acres  must  there  be  in  the  field  1 

59.  J.  Bagg  &  Co.,  becoming  insolvent,  their  indebtedness 
was  |11666|  their  assets  were  $9012.50.  What  %  of  their 
indebtedness  can  they  pay,  allowing  to  the  assignees  3^  on 
the  amount  distributed  to  the  creditors  ? 

60.  The  Treasurer  of  the  State  of  Pennsylvania,  Nov.  30, 


ARITHMETICAL   EXAMPLES.  167 

1863,  made  the  following  report  of  the  finances  of  the  State : 
Balance  in  treasury,  Nov.  30,  1861,  $1592637.72;  receipts 
from  ordinary  sources,  to  Nov.  30,  1862,  $4047822.39 ;  from 
extraordinary  sources,  $1163925.24;  payments  to  the  same 
date,  $4590509.25.  Required  the  balance  in  treasury,  Nov. 
30,  1862. 

61.  Receipts  for  the  year  ending  Nov.  30,  1863,  $4289- 
451.65;  payments  to  the  same  date,  $4314964.05.  How 
much  less  in  the  treasury,  Nov.  30,  1863,  than  Nov.  30, 
1862 1 

62.  I  -wish  to  pay  a  bill  in  Naples  of  1500  ducats ;  the 
direct  exchange  is  $1.40  =  1  ducat;  the  exchange  on  London 
is  171^;  of  London  on  Paris  is  £1=26  francs;  of  Paris  on 
Naples  is  4|  francs =1  ducat.  What  is  the  difference  between 
the  direct  and  circuitous  exchange  1 

63.  A  square  pyramid  of  cannon-balls  has  12  on  each  side 
at  the  base.     How  many  balls  in  the  pyramid  ? 

64.  How  many  pounds  of  sugar  at  8,  13,  and  14  cts.  per 
pound,  may  be  mixed  with  3  pounds  at  9|  cts.,  2  pounds  at 
8^  cts.,  and  4  pounds  at  14  cts.  a  pound,  so  as  to  gain  16^  by 
selling  the  mixture  at  14A  cts.  per  pound  ? 

65.  What  is  the  difference  between  the  true  and  bank  dis- 
count of  $3000,  payable  in  120  days  at  8A^1 

66.  Two  churches  stand  on  opposite  sides  of  a  street  120 
feet  wide;  the  height  of  the  towers  is  70  and  95  feet,  re- 
spectively. What  is  the  distance  from  the  top  of  one  tower 
to  the  top  of  the  other  1  and  what  is  the  distance  from  the 
top  of  each  to  the  base  of  the  opposite  church  1 

67.  What  is  the  hour  when  |  of  the  time  past  noon  is  |  of 
the  time  till  midnight  1 

68.  E,  F,  and  G  start  from  the  same  point  and  in  the  same 
direction  to  walk  around  a  trotting  course  1  mile  in  circum- 
ference ;  E  takes  60  steps,  of  26  inches  each,  a  minute ;  F,  90 
steps,  each  28  inches  in  length;  and  G,  120  steps,  each  32 
inches  in  length.     What  distance  must  each  travel,    and  how 


168  ARITHMETICAL    EXAMPLES. 

long,  before  they  will  be  together  again  at  the  point  of  start- 
ing] 

69.  A  man  wishes  to  tether  his  horse  to  a  stake,  so  that  it 
may  graze  on  |  of  an  acre.  What  must  be  the  length  of 
rope  ? 

70.  A  bought  a  house  of  B,  and  gave  him  his  bond  for 
86000,  dated  April  1,  1860,  payable  in  5  equal  annual  install- 
ments of  $1200,  the  first  to  be  paid  April  1,  1861 ;  A  took 
up  his  bond  April  1, 1863,  semi-annual  discount  at  the  rate  of 
1%  per  annum  on  the  payments  due  after  April  1,  1863, 
being  deducted.     What  sum  canceled  the  bond  % 

71.  What  is  the  compound  interest  of  II  for  143  years, 
allowing  it  to  double  once  in  11  yr.  11  mo '? 

72.  A  servant  being  ordered  to  purchase  40  animals  for 
140,  brought  home  calves  at  $4,  lambs  at  $1.00,  and  kids  at 
$.50  each.     How  many  of  each  kind  did  he  purchase  ? 

73.  If  I  borrow  $1000,  and  agree  to  pay  6^  at  the  end  of 
each  year  for  the  use  of  it,  and  at  the  end  of  18  months  it  is 
called  for,  how  much  do  I  strictly  owe  ? 

74.  If  a  cannon-ball,  8  in.  in  diameter,  weigh  128  pounds, 
what  is  the  diameter  of  a  ball  weighing  250  pounds  ? 

75.  I  have  sugars  worth  12,  14,  16,  and  18  cents  a  pound. 
How  many  pounds  of  each  kind  may  I  mix  to  make  a  barrel 
of  260  pounds,  which  I  can  sell  at  $.16^  per  pound,  and  gain 
10^? 

76.  A  and  B  gain  in  business  $5040,  of  which  A  is  to  have 
10^  more  than  B.     Required  the  share  of  each  1 

77.  What  length  of  fence  will  inclose  a  circular  field  con- 
taining 10  acres? 

78.  An  ox,  whose  girth  is  8  fl.,  weighs  1500  lb;  what  is 
the  girth  of  another  ox  that  weighs  632  lb.  13  oz.  ? 

79.  X  and  Y  entering  into  partnership,  X  at  first  put  in 
$1600,  and  after  1  year  added  $400  to  his  capital;  Y  put  in 
$2000,  and  after  6  months  withdrew  $800  j   at  the  end  of  2 


ARITHMETICAL    EXAMPLES. 


169 


years  they  have  gained  $6960.     Required  each  one's  share  of 
the  gain  1 

80.  How  many  miles  of  furrovr,  1  ft.  3  in.  wide,  must  be 
turned  in  plowing  a  rectangular  field,  whose  width  is  30  rods, 
and  whose  length  is  10  rods  less  than  its  diagonal  ? 

81.  The  wholesale  price  of  coifee  in  New  York  in  1863  was 
S3  J  cents  per  pound,  and  the  price  in  1847  was  |  of  a  cent 
more  than  i  the  price  in  1863,  The  price  of  1  pound  in  the 
latter  year  would  have  bought  how  many  pounds  in  the  for- 
mer year  ? 


82.  The  pressure  of  air  being  15  pounds  to  a  square  inch, 
what  is  the  pressure  upon  a  pair  of  Magdeburg  hemispheres, 
8  inches  in  diameter  1 

83.  In  the  city  of  New  York  in  1862,  3198  marriages  were 
reported  to  the  city  Inspector,  and  he  estimated  the  numbei 
reported  to  be  26^  of  the  actual  number.  What  was  his 
estimate  of  the  whole  number  ? 

84.  A  park,  8  rods  square,  has  a  gravel  walk  around  it  of 
the  same  width  on  all  sides,  the  area  of  which  is  ^jVij  ^^^  ^^®^-- 
of  the  park.     Required  the  width  of  the  walk. 

85.  A  merchant  in  New  York  purchased  350  bales  of  cot- 
ton, each  containing  450  pounds,  at  8.80  a  pound,  and  shipped 
it  to  Liverpool  at  a  cost  of  16^^  for  freight  and  duties.  How 
much  in  U.  S.  currency  did  he  gain  by  selling  it  at  2s.  lOd.  a 
pound,  rate  of  exchange  17 1^^? 

86.  What  is  the  cash  balance  of  the  following  account,  Jan. 


1,  1864,  interest  at  6^ 


Richard  Rathburn. 


Dr. 

Cr. 

1863. 

1863. 

Jan.    20 

To  Mdse. 

$400     1 

March  1 

By  Cash 

$?00 

Feb.    25 

u           u 

250 

AprU    3 

"    Sundries 

500 

April    1 

»«                «4 

600     ' 

June    5 

.1           I. 

200 

June  10 

"                 " 

850 

Sept.     1 

"   Cash 

350 

Sept  12 

"                 " 

675 

Dec.      2 

"       " 

500 

Nov.    SO  1 

'>80 

170  ARITHMETICAL   EXAMPLES. 

87.  A  merchant  mixes  13  pounds  of  tea  with  7  pounds  of 
an  inferior  quality,  and  gains  20;^  by  selling  the  mixture  at 
$1.05 1  per  pound.  Allowing  one  kind  of  tea  to  be  worth  20 
cents  a  pound  more  than  the  other,  what  is  the  cost  of  each 
per  pound  1 

88.  How  much  less  will  the  fencing  of  20  acres  cost  in  the 
square  form  than  in  the  form  of  a  rectangle,  whose  breadth  is 
4  the  length,  the  price  being  $2.25  per  rod  ? 

89.  A.  Smith,  34  years  old,  insures  his  life  for  $5000,  at 
the  rate  of  $2.5232  per  $100  ;  he  dies  at  the  age  of  53.  Al- 
lowing G'^  compound  interest  on  all  premiums  paid,  how 
much  has  his  policy  actually  cost  1 

90.  How  much  bank  stock,  at  o},^  premium,  can  be  pur- 
chased for  $6240,  brokerage  A^  1 

91.  A  merchant  bought  200  bbl.  of  flour  for  $1665,  paying 
$9  per  barrel  for  first  quality,  $8  for  second,  and  $7.50  for 
third.     How  many  barrels  of  each  quality  did  he  buy. 

92.  A  cistern  15  feet  deep  will  hold  5640.192  gallons. 
"What  is  its  diameter  1 

93.  A  young  man  inherited  an  estate  of  $40000 ;  after 
spending  i  of  it,  he  invested  the  remainder  in  an  unsuccessful 
business,  losing  33] c^  gf  the  investment;  with  his  remaining 
money  he  purchased  5-20  United  States  bonds  at  par,  bearing 
G^^  interest,  payable  in  gold.  How  much  was  his  yearly  in- 
come in  currency,  gold  being  175f^  1 

94.  A  Chicago  merchant  shipped  1000  barrels  of  flour  to 
his  agent  in  New  Orleans,  directing  him  to  sell  it,  and  invest 
the  proceeds  in  cotton  ;  his  agent  sold  the  flour  at  $14  per 
bbl.,  paid  $275  charges,  and  bought  cotton  at  $.65  per  pound, 
charging  3^  commission  for  selling  the  flour  and  6%  for  buy- 
ing the  cotton.     How  many  pounds  of  cotton  did  he  buy  ? 

95.  M  and  N  arc  joint  tenants  of  a  house,  paying  $62.50 
and  $87.50,  respectively,  each  quarter  for  rent.     The  land- 


ARITHMETICAL    EXAMPLES.  171 

lord  having  raised  the  annual  rent  $100,  what  rent  must  each 
now  pay  quarterly "? 

90.  Having  placed  a  bill  of  $775  in  the  hands  of  a  col- 
lector, who  succeeded  in  obtaining  7b^  of  it,  and  charged  S'^ 
commission,  how  much  did  I  receive  1 

97.  How  much  larger  is  a  square  circumscribing  a  circle 
40  rods  in  diameter,  than  a  square  inscribed  in  the  same 
circle  1 

.  98.  A  grocer  sold  2000  gallons  of  molasses  for  $1880,  and 
gained  on  each  gallon  sold  the  cost  of  1|^  pints,  beer  meas- 
ure.    What  did  the  molasses  cost  per  gallon  1 

99.  By  the  fortification  bill  of  1863,  Congress  appropriated 
for  forts  as  follows  :  Maryland,  $200000  ;  Mississippi  River, 
\\  times  as  much  ;  Pacific  coast,  §§  of  the  two  preceding  ap- 
propriations; Florida,  X^.^  times  the  three  preceding  appro- 
priations •,  New  York,  1 1  of  the  four  appropriations  already 
mentioned;  and  New  England  |f  of  all  the  others.  How 
much  was  the  amount  of  the  bill  ? 

100.  A's  money  was  to  B's  as  2  to  3  ;  when  A  had  spent 
$40,  and  B  had  spent  40^  more  than  A,  A's  money,  minus 
$20.  was  to  B's  money,  plus  $2,  as  4  to  9.  How  much  had 
each  at  first  % 

101.  A  merchant  bought  a  certain  quantity  of  corn,  for 
which  he  paid  a  certain  sum  of  money  ;  but  on  measuring,  he 
found  only  |  §  of  the  quantity  he  expected.  He  sold  it,  gain- 
ing i  the  cost,  and  received  $2100,  which  was  at  the  rate  of 
1 2  f"*3  cents  per  bushel  more  than  he  would  have  paid  had  he 
received  the  quantity  he  expected.  How  many  bushels  did 
he  suppose  he  had  bought,  and  at  what  price  ? 

102.  How  many  thousand  shingles,  averaging  4  in.  wide, 
•and  lying  6  inches  to  the  weather,  are  required  to  cover  both 
sides  of  a  roof  36  ft.  long,  whose  rafters  are  20  f  jet  In  length  % 

103.  Andrew  Combs  purchased  of  H.  Alexander  wheat  on 
3  months  credit,  as  follows :  Apr.  5,  500  bu.,  ®  $.87A  ;  Apr. 


172  ARITHMETICAL    EXAMPLES. 

25,  300  bii.,  @  $.95  ;  June  20,  350  bu.,  ©  $1.10  ;  July  10, 
250  bu.,  @  81.05.     When  was  the  account  due  by  average? 

104.  A,  B  and  C  entered  into  partnership.  A  put  in 
$12000,  B  $8000,  and  C  $7000.  At  the  end  of  the  first  year 
A  drew  ojt  82000,  B  81000,  and  C  put  in  $3000.  At  the 
close  of  the  second  year  A  and  B  each  drew  out  $1000,  and 
C  put  in  $2000  more.  At  the  end  of  the  third  year  they  dis- 
solved partnership,  and  found  that  their  joint  property  was 
$28500.     What  was  each  partner's  share  ? 

\  105.  If  a  pipe  3  inches  in  diameter  discharge  12  hogsheads 
of  water  in  a  certain  time,  what  must  be  the  diameter  of  a 
pipe  which  will  di:;charge  48  hogsheads  in  the  same  time  1 

lOG.  If  I  buy  50  sliares  Hudson  River  R.  Jl.  stock  at  141^, 
and  50  shares  Michigan  Central  R.  R.  stock  at  139;;:^,  the  for- 
mer paying  a  semi-annual  dividend  of  4Jg^,  the  latter  of  5^; 
what  rate  of  interest  shall  I  realize  on  my  investment? 

107.  The  horizon'tal  di-tance  between  the  eaves  of  a  certain 
building  1  j  40  fc. ;  the  elevation  of  the  ridge  above  the  eaves 
is  15  ft.     AVIiat  is  the  length  of  the  raf.ers  1 

108.  If  a  man  by  laboring  15  hours  a  day  do  a  work  in  8 
days,  how  many  hours  a  day  must  he  labor  to  do  the  same  in 
10  days? 

109.  A  speculator  purchased  255^  acres  of  land  at  $45| 
per  acre,  but  was  obliged  to  sell  it  at  $23|  per  acre.  For 
how  much  more  than  his  loss  did  he  sell  it  ? 

110.  What  number,  increased  by  1,  i  and  j  of  itself, 
equals  317? 

111.  A  w^ine  dealer  desires  to  mix  20  gallons  of  wine, 
worth  -^3.50  per.  gal.,  with  wines  worth  $3.25  and  $1.80  per 
gal.,  so  as  to  form  a  mixture  of  96  gallons,  worth  $3.00  a 
gallon.     ITow  much  of  each  kind  may  he  take? 

112.  J.  Smith  bought  of  Ivison,  Phinney,  Blakeman  <^  Co., 
the  following  bills  of  goods;  Nov.  1,  1863,  a  bill  of  $750,  on  6 
mo.  credit;  Dec.  15,  1863,  a  bill  of  $300,  on  5  mo.;  Jan.  1, 


ARITHMETICAL   EXAMPLES.  173 

1864,  a  bill  of  $425,  on  4  rno. ;  Feb.  5,  1864,  a  bill  of  $275, 
on  2  mo.  What  sum  would  settle  the  account,  May  29, 
1864,  interest  at  7^'? 

113.  A  gentleman  wishes  to  set  out  a  rectangular  orchard 
of  1260  trees,  so  placed  that  the  number  of  rows  shall  be  to 
the  number  of  trees  in  a  row  as  5  to  7.  If  the  trees  are  8 
yards  apart,  how  much  ground  will  the  orchard  occupy  1 

114.  A  merchant  insures  a  ship  and  cargo  for  879325,  at 
4|^,  the  policy  covering  both  property  and  premium.  What 
is  the  value  of  the  ship  and  cargo  1 

115.  A,  B  and  C  formed  a  partnership  for  2  years ;  A  put 
in  $10000,  B  $5000,  and  C  $2500 ;  it  was  agreed  that  C 
should  receive  $1500  a  year  for  superintending  the  business. 
A  drew  out  $1000  at  the  end  of  each  quarter  for  one  year, 
and  at  the  end  of  13  months  put  in  $15000  more;  B  with- 
drew $600  at  the  end  of  each  quarter.  At  the  time  of  settle- 
ment the  net  gain  was  $22500.     Required  each  one's  share. 

116.  If  496  men,  in  5  days  of  11  hours  each,  can  dig  a 
trench  620  yd.  long,  3  yd.  wide  and  2  yd.  deep,  in  how  many 
days  of  12  hours  each  will  48  men  dig  a  trench  210  yd.  long, 
6  yd.  wide  and  3  yd.  deep  1 

117.  When  exchange  on  England  is  at  10^  premium,  and 
freight  at  Is.  3d.  per  United  States  bushel,  how  much  can  be 
paid  in  Philadelphia  for  wheat  per  bushel,  in  answering  an 
order  from  London  limited  to  £3  lOs.  per  Imperial  quarter? 

118.  In  a  pair  of  scales  a  body  weighed  32  pounds  in  one 
scale,  and  only  24^  pounds  in  the  other.  What  was  its  true 
weight  1 

119.  Suppose  a  number  of  stones  were  laid  a  rod  apart  for 
30  miles,  the  first  stone  by  the  side  of  a  basket.  What  dis- 
tance will  a  man  travel  who  gathers  them  up  one  by  one,  re- 
turning with  each  one  to  the  basket  1 

120.  A  merchant  shipped  a  cargo  of  flour,  worth  $23940, 
from  Racine  to  Liverpool.     To  insure  it  from  Racine  to  Buf- 


174  AKITHMETICAL    EXAMPLES. 

falo  he  paid  l-^fo',  from  Buffalo  to  New  York,  ^^•,  and  from 
New  York  to  Liverpool,  3|«^.  For  what  sum  must  it  be  in- 
sured to  cover  the  value  of  the  flour  and  premium  fur  the 
voyage  1 

121.  A  man  in  Cleveland  purchased  a  draft  on  St.  Louis, 
Missouri,  for  $10640,  drawn  at  60  days,  paying  110283.56. 
What  was  the  course  of  exchange  ? 

122.  A  merchant  sold  350  barrels  of  pork  for  $8662.50, 
and  gained  10^^.     What  did  the  pork  cost  him  per  barrel  1 

123.  A  gentleman  insures  his  house,  worth  $9000,  and  his 
furniture,  worth  $3500,  for  J  of  their  value  at  |^.  What 
premium  did  he  pay  1 

124.  I  have  a  circular  field  600  rods  in  circumference. 
What  must  be  the  side  of  a  square  field  that  shall  contain  the 
same  area? 

125.  A's  age  is  double  that  of  B,  and  B  is  three  times  as 
old  as  C,  and  the  sum  of  their  ages  is  70.  What  is  the  age 
of  each  one  ? 

126.  A  and  B  having  the  same  income,  A  spends  |  of  his, 
and  B,  by  spending  $200  a  year  more  than  A,  finds  himself 
at  the  end  of  5  years  $450  in  debt.  How  much  was  their 
income  1 

127.  Insert  7  geometrical  means  between  5  and  1280. 

128.  What  sum  of  money  must  be  invested  in  5-20's,  bearing 
6%  interest  in  gold,  and  purchased  at  105^,  to  produce  a  semi- 
annual income  of  $600  U.  S.  currency,  gold  being  172|^? 

129.  A  merchant  bought,  on  10  mo.  credit,  25  pieces  of 
cloth,  each  containing  30  yards,  at  |4.66f  per  yard ;  after 
keeping  the  goods  3  mo.  he  sold  them  at  $5  per  yard  on  a 
credit  of  9  mo. ;  money  being  worth  6fo,  what  was  his  net 
cash  gain  at  the  time  of  the  sale  ? 

130.  An  irregular  piece  of  land  containing  305  A.  41  P., 
was  exchanged  for  a  square  piece  containing  the  same  area. 
What  was  the  length  of  one  of  its  sides'?     If  divided  into 


ARITHMETICAL    EXAMPLES. 


/o> 


169  square  building  lots,  what  will  be  the  length  of  a  side  of 
each  ? 

131.  Bought  who.it  at  -^1.75,  §1.80  and  82.00  per  bushel. 
In  what  proportion  may  they  be  mixed  so  as  to  sell  the  mix- 
ture at  $2.15|  per  bushel,  on  3  mo.  credit,  when  money  is 
worth  10^,  and  make  a  present  gain  of  12^? 

132.  A  man  purchased  a  farm  for  83000,  and  agreed  to  pay 
principal  and  interest  in  4  equal  annual  installments.  What 
was  the  annual  payment,  interest  being  Q^  ? 

133.  At  a  certain  time  between  one  and  two  o'clock,  the 
minute  hand  is  between  2  and  3,  and  within  an  hour  the  hands 
will  exactly  change  places.  AVhat  is  the  first  mentioned 
time  ? 

134.  What  sum  of  money,  with  its  semi-annual  dividends 
of  4^  invested  with  it,  will  amount  to  $25000  in  3  years  1 

135.  When  gold  is  quoted  at  162^,  what  is  the  value  in 
gold  of  a  U.  S.  note  of  the  denomination  of  $10? 

136.  Account  sales  of  100  pipes  of  gin,  received  per  sliip 
Hispaniola,  from  Havana,  on  %  of  Tyler,  Jones,  &  Co. 


I860. 
April    15 
May        5 
June     28 


April  1 
1 
1 

June    28 


Sold    32 

"     40 
"      28 


41  GO  gal.  at  $1.05,  on  30  days, 

5240    "     at     1.02,  cash, 

3650    "     at    1.00,     "     


CHARGES- 

To  Freight  and  Primage $136.76 

"  Wharfage  and  Cartage 48.54 

"  Duty  Bonds,  at  60  days 3207.07 

"  Storage  from  April  1,  viz.  : 

On   32  Pipes,     2wks..  64  wks, 
"    40      "         6    "    ..200    " 
"    '-3      »       13     "   ..364    " 

100      "       equal  to    628    "  at  6c 37.68 

"  Commission  on  $13362.80,  at  2^  per  cent 334  07 

"  Guaranty  on  $4368,  at  2i  per  cent 109.20 


5344 
3650 


13362 


8873 


What  are  the  net  proceeds  of  the  above  account,  and  when 
due? 

Note. — The  time  for  which  storage  is  charged  on  each  part  of  the 
shipment  is  the  interval,  reduced  to  weeks,  between  Apr.  1,  when  the 
pipes  were  received  into  store,  and  the  date  of  sale.  Every  fraction  of  a 
week  is  reckoned  a  full  week. 


176  ARITHMETICAL   EXAMPLES. 

137.  A  walk  9  ft.  wide  surrounds  a  square  garden;  the 
area  of  the  walk  being  |  of  an  acre,  what  is  a  side  of  the  in- 
closed square  1 

138.  A  man  in  Worcester,  Mass.,  has  $2400  due  him  in 
Chicago.  How  much  more  will  he  realize  by  making  a  draft 
for  this  sum  on  Chicago,  and  selling  it  at  ^^  discount,  than  by- 
having  a  draft  on  Worcester  remitted  to  him,  purchased  in 
Chicago  for  this  sum  at  |^  premium  ? 

139.  A  father  divides  an  estate  worth  15555.66  between  his 
two  sons,  giving  the  elder  J  more  than  the  younger.  How 
much  is  each  son's  share  ? 

140.  M  began  business  with  $1000 ;  four  months  after,  S 
entered  into  partnership  with  him,  and  put  in  6  houses,  each 
of  the  same  value ;  at  the  close  of  the  year  their  profits  were 
$3000,  of  which  S's  share  was  $2000.  What  were  his  houses 
each  valued  at  ? 

141.  A  grocer  mixed  4  pounds  of  tea  at  $1.20  with  3 
pounds  at  $1.40,  1  pound  at  $2.20,  and  2  pounds  at  $2.40. 
What  per  cent,  profit  will  he  make  by  selling  the  mixture  at 
$2.00  per  pound  ? 

142.  A  farmer  has  sheep  worth  $4,  $6  and  $8  a  head  re- 
spectively. How  many  of  each  kind  must  he  sell  to  realize 
an  average  price  of  $6.25  a  head  1 

143.  What  is  the  distance  from  one  corner  of  a  cubical 
block  to  the  opposite  diagonal  corner,  the  side  of  the  cube 
being  5  feet  ? 

144.  A  and  B  traded  in  company.  A  put  in  $845  for  300 
days,  and  received  |  of  the  gain.  The  number  of  dollars 
which  B  put  in  was  equal  to  the  number  of  days  it  was  em- 
ployed in  trade.     What  was  B's  capital  ? 

145.  Insert  5  arithmetical  means  between  2  and  4. 

146.  If  a  stack  of  hay  8  ft.  in  hight  weigh  8  cwt.,  what  is 
the  weight  of  a  similar  stack  that  is  24  ft.  in  hight  ? 

147.  Allowing  5fo  of  the  hay  in  the  stack  last  mentioned  to 


ARITHMETICAL   EXAMPLES.  177 

be  worthless,  what  is  the  value  of  the  remainder  at  $14  per 
ton  ? 

148.  There  is  a  circular  field  100  rods  in  circumference. 
How  far  will  a  person  have  traveled,  in  setting  the  border 
with  trees  1  rod  apart,  when  the  last  tree  is  set,  provided  he 
returns  to  the  point  of  starting  for  each  tree,  and  always 
travels  around  in  the  same  direction  ? 

149.  A  man  engaged  a  boy  at  the  rate  of  $.25  for  the  first 
day,  $.30  for  the  second,  $.35  for  the  third,  and  so  on,  in- 
creasing his  wages  5  cents  per  day.  How  many  days  must 
the  boy  work  that  his  average  wages  may  be  $.60  per  day  ? 

150.  The  triangular  gable  of  a  certain  building  has  a  base 
of  44  ft.  and  an  altitude  of  18  ft.  How  many  square  feet  of 
boards  will  cover  the  two  gables  ? 

151.  If  I  rent  a  house  which  cost  $9000,  for  $900  a  year, 
and  lay  out  $150  in  repairs,  what  ^  interest  do  I  receive  ? 

152.  A  man  bought  |  of  a  vessel,  and  sold  |  of  his  share 
for  $11700,  which  was  30^  above  the  cost.  What  was  the 
cost  of  the  vessel  ? 

153.  A  merchant  sold  238  hhd.  of  sugar,  each  containing 
963  pounds  net  weight,  at  13  cents  a  pound,  on  4  months' 
time,  and  immediately  got  the  paper  discounted  at  a  bank  at 
Ifo.     How  much  money  did  he  receive  1 

154.  If  6i  oz.  of  bread  can  bfe  bought  for  4~d.  when  corn 
is  5s.  6d.  per  bushel,  what  weight  of  bread  can  be  bought  for 
Is.  3d.  when  the  price  per  bushel  is  6s.  3d.  1 

155.  A  captain,  commanding  a  company  of  100  men  who 
had  performed  a  daring  exploit,  being  asked  what  reward 
could  satisfy  him,  replied,  "  a  cent  for  every  different  file  of 
ten  men  that  can  be  made  with  my  company."  What  did 
his  demand  amount  to  ? 

156.  II.  Jones  &  Co.  failed  in  business.  They  owed  A 
$4000,  B  $5000,  and  C  $7000;  their  assets  amounted  to 
$11200,  and  the  charges  of  the  assignees  were 


178  ATIITHMETICAL    EXAMPLES, 

amount  distributed.     What  %  did  they  pay  ?  and  how  much 
did  each  creditor  receive  1 

157.  A  lot  of  land,  containing  15  acres,  is  30  rods  wide, 
and  is  a  plane  inclining  in  the  direction  of  its  length ;  one  end 
being  120  feet  higher  than  the  other.  How  many  acres  of 
surface  does  the  inclined  plane  contain  ? 

158.  By  selling  sugar  at  $15  per  cwt.  I  gain  20^;  what  fo 
should  I  gain  by  selling  it  at  $13.50  per  cwt.  ? 

159.  A  man  paid  annually  $10  for  tobacco  from  the  age  of 
14  until  he  was  50,  when  he  died,  and  left  $1000  for  his  heirs. 
What  sum  might  he  have  left  them  had  he  dispensed  with 
tobacco,  and  loaned  the  money  thus  saved  at  the  end  of  each 
year  at  6^  compound  interest  ? 

160.  Two  ships  start  from  New  York  at  the  same  time; 
one  sails  due  south  at  the  rate  of  12  miles  an  hour,  and  the 
other  due  east  at  the  rate  of  9A  miles  an  hour.  How  flir 
apart  are  they  in  48  hours  ? 

161.  A.  Banks  received  a  legacy  of  $8000,  $800  of  which 
was  payable  in  9  months,  $800  in  one  year,  and  the  balance 
in  two  years  ;  but  the  executor  being  willing  to  make  present 
payment,  discounting  at  7^,  what  ought  he  to  receive  % 

162.  A  merchant  receives  10000  barrels  of  flour  to  sell  on 
commission,  and  is  directed  to  invest  the  proceeds  in  United 
States  demand  notes  bearing  7 /^^  interest;  he  pays  $759 
charges,  and  sells  the  flour  at  $9  per  barrel  ;  his  commission 
is  8^  on  the  sales.  What  amount  of  Treasury  Notes  can  he 
buy  at  36^  premium,  brokerage  ^^%  ? 

163.  The  fore  wheels  of  a  carriage  are  3  ft.  6  in.  in  diame- 
ter, and  the  hind  wheels  4  ft.  9  in.  How  many  times  mu<t 
each  revolve  in  running  from  Springfield  to  Chicago,  a  dis- 
tance of  204  miles  1 

164.  The  exterior  diameter  of  a  spherical  shell  is  12  in., 
and  the  shell  is  1  in.  thick.  What  is  the  difference  between 
the  exterior  and  interior  surfaces  1 


AKITHMETICAL   EXAMPLES.  170 

165.  "What  was  the  balance  of  the  folio  whig  account,  Jan, 
1,  1864,  money  being  worth  7%^ 

B.  Newton  in  account  current  with  J,  Dailey. 


Dr. 

Cr. 

1S63. 

1 

1S63.      1 

1 

Jan.      1 

To  Mdse. 

$2-25 

00 

Feb. 

10 

By  Cash, 

$150 

00 

Mar.  10 

u      It 

3T0 

50 

■  1 

Mar. 

'25  1 

"       " 

300 

00 

June  15 

U           i( 

550 

00 

July 

1   1 

"   Mdse. 

430 

50 

Sept.     1 

7-20 

'2i> 

11 

Sept. 

1  J 

"   Cash, 

500 

Nov.     5 

160 

'25 

1 

166.  What  is  the  present  worth  of  an  annuity  of  8960  in 
perpetuity  at  Gfo  1 

167.  If  9|  acres  of  land  are  bought  for  $301  y^^,  what  will 
be  the  cost  of  196|  acres  of  land,  worth  |  as  much  per  acre*? 

168.  A  ball  falling  from  a  height  of  12  ft.  bounds  6  ft.  by 
its  elasticity,  and  again  falling,  bounds  3  ft.,  and  so  on,  bound- 
hior  each  time  ^  as  high,  as  it  falls.  How  far  will  the  ball  fall 
before  coming  to  a  state  of  rest  1  and  what  will  be  the  dis- 
tance of  all  the  successive  bounds  ? 

169.  For  what  sum  must  a  note  be  drawai  at  3  mo.  that 
the  proceeds,  when  discounted  at  a  bank  at  7^,  shall  be 
8981.91P 

170.  A  Cincinnati  merchant  bought  a  quantity  of  pork  for 
86000,  and  forwarded  it  to  New  York,  paying  9fc  of  the  cost 
for  freight  and  charges ;  it  was  then  sold  by  an  agent  at  an 
advance  of  30^  on  the  original  cost,  commission  5fc.  How 
much  was  the  net  gain  ? 

171.  A  broker  bought  90  shares  of  $100  each  of  New  York 
Central  R.  R.  stock  at  127,^,  and  sold  the  same  at  136^;;^. 
How  much  was  the  net  gain  ? 

172.  A  circular  cistern  7  ft.  in  diameter  has  a  capacity  of 
2400.06  gallons.     What  is  its  depth  ] 

173.  How  many  pupils  in  a  school  when  I  attend  the  gram- 
mar department,  |  the  intermediate,  and  the  remainder, 
which  is  34  less  than  S  the  whole  number  of  scholars,  attend 
the  primary  1 

174:.  A  man  insured  his  house,  valued  at  $18000,  and  fur- 


180  ARITHMETICAL    EXAMPLES. 

niture,  worth   $7000,   for  /g  of  their  value,  at   ^'/o.     What 
premium  did  he  pay  1 

175.  H  and  J  traded  in  company ;  II  put  in  $8000,  and  J 
$20000  ;  they  were  to  share  the  gains  or  losses  equally  ;  at  the 
end  of  two  years  they  dissolved  partnership,  and  found  their 
net  capital  to  be  122500.     What  was  each  one's  share  1 

176.  A  person  exchanged  180  shares  of  6  per  cent,  stocks, 
at  80^,  for  10  per  cent,  stocks,  at  125^.  How  much  was  his 
yearly  income  increased  1 

177.  If  a  man  dig  a  square  cellar  that  measures  5  ft.  each 
way  in  one  day,  how  long  will  it  take  him  to  dig  one  meas« 
uring  10  ft.  each  way  ? 

178.  Sold  coffee  at  13^  cents  a  pound,  and  thereby  lost  20^ 
on  the  cost ;  afterward  sold  a  quantity  of  the  same  for  $455, 
and  gained  SOfo.  What  quantity  was  sold?  and  at  what 
price  ? 

179.  The  diameter  of  the  sun  is  110  times  as  large  as  that 
of  the  earth.  The  volume  of  the  sun  is  how  many  times  as 
large  as  the  volume  of  the  earth  ? 

180.  Received  an  invoice  of  crockery,  5  per  cent,  of  which 
was  broken ;  paid  a  duty  of  20  per  cent,  upon  the  remainder. 
For  what  per  cent,  above  the  invoiced  value  must  it  be  sold 
to  gain  25  per  cent,  on  the  whole  cost  1 

181.  The  length  of  a  rectangular  field  containing  13  A.  3  R. 
5  P.  is  to  its  breadth  as  9  to  5.     What  are  its  dimensions  ? 

182.  A  merchant  in  New  York  in  1863  gave  $5044.725  for 
a  bill  of  exchange  on  London  for  £650.  What  was  the  rate 
of  exchange  ? 

183.  A  gentleman  laid  out  a  garden  in  the  form  of  an 
ellipse,  its  longer  diameter  being  8  rods,  and  its  shorter  5 
rods.     V/hat  was  the  area  of  the  garden  1 

184.  If  stock,  bought  at  20^  premium,  pay  6|^  on  the 
investment,  what  ^  will  it  pay  if  bought  at  5^  discount  ? 

185.  How  many  yards  of  plastering  in  a  room  21  ft.  9  in. 


ARITHMETICAL    EXAMPLES.  181 

long,  16  ft.  6  in.  wide,  and  10  ft.  8  in.  high,  there  being  3 
doors,  each  8  ft.  3  in.  by  4  ft.  3  in. ;  2  windows,  each  7  ft. 
6  in.  by  4  ft.  6  in. ;  1  fire-place  5  ft.  2  in.  by  3  ft.  6  in.,  and 
a  base-board  8  in.  wide  ? 

186.  A  produce  dealer  bought  30000  bushels  of  corn  at 
$1.55  per  bushel,  paying  $450  charges,  and  $225  storage;  he 
immediately  sold  it  at  25^  advance  on  the  entire  cost  on  90 
days'  time.  At  what  price  per  bushel  did  he  sell  the  corn  1 
and  what  fo  did  he  gain  at  the  time  of  the  sale,  money  being 
worth  7fo  1 

187.  If  76  pounds  of  sugar  cost  £4  3s.  lid.,  how  many 
pounds  of  sugar  worth  |  as  much  per  pound  can  be  purchased 
with  £2  17s.  5d.  ? 

188.  The  present  worth  of  an  annuity  to  be  continued  10 
years  at  6  per  cent.,  compound  interest,  compounded  annu- 
ally, is  $7360.08.     What  is  the  annuity  ? 

189.  A  pipe  i|  inches  in  diameter  will  fill  a  cistern  in  40 
minutes.  In  what  time  will  6  pipes,  each  |  of  an  inch  in 
diameter,  fill  a  cistern  of  three  times  the  capacity  ? 

190.  "What  will  the  gilding  of  a  ball  1  ft.  9  in.  in  diameter 
cost,  at  2s.  6d.  per  square  inch  1 

191.  A  cubic  inch  of  lead  weighs  |  of  a  pound.  How 
many  feet  of  lead  pipe  can  be  made  from  100  pounds  of  lead, 
the  caliber  of  the  pipe  being  |  of  an  inch,  and  its  thickness  | 
of  an  inch  ? 

192.  Divide  $1048.80  among  3  persons,  in  such  a  manner 
that  the  share  of  the  second  may  be  |  greater  than  that  of  the 
first,  and  the  share  of  the  third  -^  greater  than  that  of  the 
second. 

193.  A,  L  and  W  bought  a  vessel,  A  taking  -J  interest,  L 
-J,  and  W  the  remainder ;  during  the  year  following  A  paid  for 
expenses  $1850,  and  received  $3325  cash  returns;  L  paid  out 
$1320,  and  received  $4500 ;  W  paid  $2600,  and  received 
$1570.     At   the   close   of  the   year,  L  sold  the  vessel  for 


182  ARITHMETICAL   EXAMPLES. 

$24500.     Interest  not   being  reckoned   on  receipts  and  ex- 
penditures, how  much  must  L  pay  to  A  and  W  1 

194.  The  contents  of  a  cubical  block  of  granite  are  4913 
solid  feet.     What  are  the  superficial  contents? 

195.  A  offers  to  loan  to  B  11000  for  6  mo.,  at  10^ ;  the 
legal  rate  is  7^.  For  what  sum  must  the  note  be  drawn  that 
the  amount  of  it  at  7^  will  equal  the  amount  of  $1000  at  10,^ 
for  the  given  time  ? 

196.  The  duty  at  30^  on  a  quantity  of  coffee  in  bags,  each 
weighing  175  pounds  gross,  and  invoiced  at  $.14  a  pound, 
was  $3491.25.  Tare  being  5^,  how  many  bags  were  im- 
ported ? 

197.  A  father  divided  his  property  among  his  four  sons, 
directing  that  A  should  have  |6  as  often  as  B  $5,  C  $3  as 
often  as  A  $4,  and  T>  $8  as  often  as  B  $9.  What  was  the 
amount  of  property^  D's  share  being  $6000  ? 

198.  J.  Ellis  &  Co.  sold  Thomas  Strong  goods  to  the 
amount  of  $2500,  on  6  months'  credit ;  Strong  paid  $350  in 
2  months,  $600  in  4  months,  $500  in  7  months,  and  the  bal- 
ance in  12  months.  What  amount  was  due  at  the  time  of 
settlement,  interest  7fo  1 

199.  What  %  in  advance  o^  the  cost  must  a  merchant 
mark  his  goods  so  that,  allowing  4fo  of  his  sales  for  bad  debts, 
an  average  credit  of  3  months,  and  8^  of  the  goods  for  ex- 
penses, his  net  gain  may  be  15^  of  the  first  cost  of  the  goods, 
money  being  worth  7%  1 

200.  What  is  the  present  worth  of  an  annuity  of  $1200  in 
reversion  7  years,  and  continuing  13  years,  at  6^  ? 

201.  The  perpendicular  height  of  a  conical  glass  is  8  in., 
and  its  diameter  at  the  top  is  5  in.  How  much  water  will  it 
hold? 

202.  What  costs  a  bill  on  London  for  £800  17s.  6d.,  when 
the  rate  of  exchang'e  is  9^^  premium  ? 

203.  A  miller  grinds  500  bushels  of  provender,  worth  75 


ARITHMETICAL   EXAMPLES.  183 

cents  a  bushel,  from  40  bushels  of  rye,  worth  90  cents  a 
bushel,  and  from  oats  worth  60  cents,  corn  worth  85  cents, 
and  barley  worth  80  cents  a  bushel.  How  many  bushels  of 
oats,  corn,  and  barley  may  he  take  ? 

204.  A  gentleman  purchased  an  annuity  of  81000,  to  con- 
tinue 20  years,  at  Q^o,  compound  interest.  What  did  it  cost 
him? 

205.  A  and  B  engage  in  trade;  A  puts  in  $10030,  and  at 
the  end  of  5  months  takes  out  a  certain  sum ;  B  puts  in 
$6000,  and  after  3  months  puts  in  $4000  more ;  at  the  end  of 
the  year,  A's  gain  is  $1800,  and  B's  $2250.  What  sura  did 
A  withdraw  at  the  end  of  5  months? 

206.  A  merchant  sold  48  yards  of  gingham  at  33 J-  cents 
per  yard,  12  pieces  of  sheeting,  each  containing  33  yards,  at 
25  cents  per  yard,  and  received  in  payment  40  bushels  of 
oats  at  62i  cents  per  bushel,  and  the  balance  in  money. 
How  much  money  did  he  receive  ? 

207.  If  the  interest  of  $691.04  for  1  mo.  3  da.  is  $3,167, 
what  will  be  the  interest  of  $640.50  for  10  mo.  26  da.,  at 
twice  the  rate  1 

208.  S.  F.  Root  bought  50  shares  of  bank  stock  at  an  ad- 
vance of  5f^  on  the  par  value  of  $100.  From  the  time  of 
purchase  until  the  end  of  3  yr.  9  mo.  he  received  a  semi-an- 
nual dividend  of  3^^,  when  he  sold  the  stock  at  a  premium 
of  10^.  Money  being  Gfi  compound  interest,  how  much  did 
he  gain  ? 

209.  My  garden  is  11  rods  7|  feet  long,  and  9  rods  15  J^ 
feet  wide.  What  is  the  length  of  the  longest  rails  that  can  be 
used  in  fencing  it,  allowing  the  end  of  each  rail  to  lap  by  the 
other  5  in.,  and  all  the  panels  to  be  of  equal  length  ?  How 
many  rails  will  fence  the  garden,  if  6  rails  are  allowed  to 
each  panel  1 

210.  If  4096  men  are  formed  into  an  oblong,  with  4  times 
as  many  men  in  rank  as  in  file,  how  many  will  there  be  in 
rank  and  file  1 


184  ARITHMETICAL    EXAMPLES. 

211.  A  gentleman  purchases  a  farm  for  110000,  which  he 
sells  after  a  certain  number  of  years  for  $14071,  making  on 
the  investment  5^  compound  interest.  He  now  invests  his 
money  in  a  perpetuity,  which  is  in  reversion  1 1  years  from 
the  date  of  purchasing  the  farm.  Allowing  6%  compound 
interest  for  the  use  of  monev,  find  the  annuity  and  the  length 
of  time  he  owns  the  farm. 

212.  Three  numbers  are  to  each  other  as  3,  5  and  7,  and 

their  continued  product  is  2835.     Required  the  numbers. 

213.  What  sum  must  be  invested  in  8  per  cent,  stocks,  at 
130;^,  to  produce  an  annual  income  of  12000? 

214.  The  shadow  of  a  steeple  measured  8  rd.  3  yd.  1  ft. 
and  6  in.  in  length,  at  the  same  time  when  the  shadow  of  a 
man  6  ft.  high  measured  4  ft.  9  in.  Required  the  height  of 
the  steeple. 

215.  J.  Smith  owes  C.  Brown  $2000,  to  be  paid  in  equal 
annual  payments  of  $400  each ;  Smith,  not  being  able  to  meet 
these  payments  at  their  maturities,  and  having  an  estate  12 
years  in  reversion,  arranges  with  Brown  to  wait  till  he  enters 
upon  his  estate,  when  he  is  to  pay  him  the  whole  sum  with 
compound  interest  at  7^.  What  sum  will  Brown  then  re- 
ceive ? 

216.  J.  Clarke  bought  of  Claflin  &  Mellen  the  following  bill 
of  goods:  June  1,  a  bill  of  $650,  on  4  months;  Sept.  15,  a 
bill  of  $800,  on  3  months;  Oct.  10,  a  bill  of  $1200,  on  1 
month.     What  was  the  equated  time  of  payment? 

217.  If  a  cable  3  inches  in  diameter  will  sustain  a  weight 
of  18000  pounds,  what  weight  can  be  sustained  by  a  cable 
15.708  inches  in  circumference'? 

218.  Divide  $2000  between  A  and  B,  so  that  A's  money 
shall  be  |  of  B's. 

219.  An  estate  of  $60000  was  to  be  divided  among  a  wife, 
son  and  two  daughters,  as  follows :  The  wife  was  to  have 
$5000  more  than  the  son,  the  son  $10000  more  than  the  elder 


ARITHMETICAL    EXAMPLES.  185 

daughter,    and    the    elder    daughter   $5000   more   than    the 
younger.  '  How  much  should  each  receive  1 

220.  How  many  acres  in  a  triangular  field  whose  sides  are 
respectively  40,  48  and  54  rods  in  length  ? 

221.  A  son,  having  asked  his  father  of  his  age,  was  answered, 
"  I  of  my  age  is  twice  your  age,  and  the  difference  of  our 
ages  is  22  years."     Eorjuirad  their  rospectivo  agc^s. 

222.  A  boy  in  flying  his  kite  got  it  entangled  in  the  vane 
of  a  steeple;  the  string  broke  close  to  the  kite;  by  measuring 
he  found  that  he  stood  450  feet  from  a  point  directly  under 
the  vane,  and  had  out  485  feet  of  string.  "What  was  the 
height  of  the  steeple  ? 

223.  In  digging  a  circular  pond,  70  yards  in  diameter,  294- 
407.19  cubic  feet  of  earth  were  excavated..  To  what  depth 
was  the  pond  dug  1 

224.  A  grocer  mixed  300  pounds  of  sugar  at  14  cents  a 
pound,  with  200  pounds  worth  15  cents  a  pound,  and  250 
pounds  at  12  cents  a  pound.  AVhat  must  be  his  price  per 
pound  to  gain  2b^  on  the  cost  1 

225.  If  the  sum  produced  by  adding  4,  g  and  f  of  a  num- 
ber to  itself  be  multiplied  by  3,  the  product  will  be  6834. 
What  is  the  number  ? 

226.  A  merchant  in  New  York  imports  from  Havana  200 
hhd.  of  W.  I.  molasses,  each  containing  63  gallons,  invoiced 
at  8.30  per  gallon ;  150  hhd.  of  B.  coffee  sugar,  each  contain- 
ing 500  pounds,  invoiced  at  $.05  per  pound  ;  80  boxes  of 
lemons,  invoiced  at  $2.50  per  box ;  and  75  boxes  of  sweet 
oranges,  invoiced  at  $3.00  per  box.  AVhat  was  the  whole 
amount  of  duty,  estimated  at  24;^  on  molasses  and  sugar,  and 
at  8^  on  lemons  and  oranges  ? 

227.  Sicrht  exchanfre  on  New  Orleans  for  $5000  cost  $5075. 
What  was  the  course  of  exchange  1 

228.  A  man  paid  $165  to  55  laborers,  consisting  of  men, 
women  and  boys ;  to  the  men  he  paid  $5  a  week,  to  the  wo- 


186  ARITHMETICAL    EXAMPLES. 

men   $1   a  week,  and  to   the  boys   $i  a  week.     How  many- 
were  there  of  each  1 

229.  A  and  B  traded  together;  A  put  in  $540  for  480 
days,  and  received  ^  of  the  gain ;  and  the  number  of  dollars 
which  B  put  in  was  equal  to  the  number  of  days  it  was  em- 
ployed in  trade.     What  was  B's  capital  ? 

230.  What  is  the  present  value  of  a  reversionary  lease  of 
$100,  commencing  14  years  hence,  and  to  continue  20  years, 
compound  interest  at  5  per  cent.  1 

231.  If  a  cistern  6  feet  in  diameter  hold  80  barrels  of  wa- 
ter, what  must  be  the  diameter  of  a  cistern  of  the  same  depth 
to  hold  1280  barrels  ? 

232.  A  gentleman  in  Boston  drew  on  Wurtemberg  for 
6000  gilders  at  $.415  per  gilder.  How  much  more  would  he 
have  received  if  he  had  ordered  remittance  to  Loudon,  and 
thence  to  New  York,  exchange  at  Wurtemberg  on  London 
being  11|  gilders  per  £1,  and  at  London  on  New  York  9|^ 
in  favor  of  sterling,  brokerage  at  l^fo  in  London  for  re- 
mitting ? 

233.  Two  boys,  each  12  years  old,  have  certain  sums  of 
money  left  to  them ;  the  sum  left  to  one  is  put  out  at  7% 
simple  interest,  the  sum  lefo  the  other  at  6^  compound  inter- 
est, compounded  semi-annually,  and  the  amount  of  each  boy's 
money  will  be  12000  when  he  is  21  years  old.  Y/hat  is  the 
sum  left  to  each  boy  ? 

234.  Find  the  sum  of  21  terms  of  the  series,  5,  4|,  4i,  etc. 

235.  A  man  traveled  13  days;  his  last  day's  journey  was 
80  miles,  and  each  day  he  traveled  5  miles  more  than  on  the 
preceding  day.  How  far  did  he  travel,  and  what  was  his  first 
day's  journey  ? 

236.  Find  the  12th  term  of  the  series,  30,  15,  7]-,  etc. 

237.  Bought  12  yards  of  cloth  for  $15.  How  many  yards 
must  I  buy  at  $1|  and  ||  a  yard,  that  the  average  price  of 
the  whole  may  be  $1|  ? 


ARITHMETICAL   EXAMPLES.  187 

238.  A  man  bequeathed  his  property,  amor.n'jin^  to  130000, 
to  his  wife  and  three  children  as  follows :  The  wife  was  to 
have  I,  and  the  remainder  was  to  be  divided  so  that  the  shares 
of  the  children  at  simple  interest  at  Q^  should  all  amount  to 

'the  same  sum  when  they  were  18  years  old ;  the  ages  of  the 
children  were  respectively  4  yr.,  5  yr.  6  mo.,  and  7  yr.  3  mo. 
What  was  the  share  of  each  child  ? 

239.  What  sum  must  be  invested  in  United  States  10-40's, 
bearing  5^  interest,  payable  in  gold,  purchased  at  par,  to  pro- 
duce a  semi-annual  income  of  $400  U.  S.  currency,  when  gold 
is  quoted  at  175^  ? 

240.  Imported  12  casks  of  wine,  each  containing  42  gallons 
invoiced  at  83.25  per  gallon  ;  paid  $96  for  freight,  and  a  duty 
of  40^.  How  much  shall  I  gain  ^  in  selling  the  whole  for 
$2747.58? 

241.  H.  Derby  contracted  to  dig  a  trench  1000  yd.  long,  in 
24  days.  Having  employed  54  men  for  15  days,  he  found 
that  only  450  yd.  had  been  dug.  How  many  more  men  must 
he  employ  to  finish  the  trench  according  to  the  contract  1 

242.  The  duty  of  a  garrison,  consisting  of  5  companies, 
containing  respectively  40,  50,  60,  70  and  80  men,  requires 
90  men  each  day.  What  number  must  each  company  fur- 
nish 1 

243.  $750.  MlDDLEFIELD,  Sept.  1,  1858. 

Six  months  after  date  I  promise  to  pay  H.  Harger  or  order, 
seven  hundred  fifty  dollars,  for  value  received,  with  interest. 

John  Joslyn. 

Indorsed  as  follows:  March  1,  1859,  $200 ;  June  16,  1859, 
$100;  Jan.  1,  1860,  $225.     What  was  due  Oct.  19,  1862? 

244.  The  duty  on  an  invoice  of  300  dozen  London  porter, 
at  30^,  was  $190.512 ;  breakage,  2fo.  Kequired  the  invoiced 
price  per  dozen. 

245.  In  how  many  different  ways  may  the  letters  of  the 
alphabet  be  arranged,  taking  15  each  time? 


188 


ARITHMETICAL   EXAMPLES. 


246.  What  is  the  equated  time  for  paying  the  balance  of 
the  following  account  ? 

J.  Jones,  m  account  with  B.  Day. 


Dr. 

Cr. 

1862. 

1862. 

1 

— ' 

Jan.      1 

To  Mdse.  on  6  mo. 

$350 

GO 

April    1 

By  Cash, 

1     $-250 

00 

March  1 

(1                 H.                   ii.        (4 

■240 

00 

May      6 

"        " 

200 

00 

April  15 

"        "          4    " 

1     175 

00 

June   30 

((               u 

300 

00 

June   20 

3    " 

1     280 

00 

Aug.      1 

2    " 

400 

247.  How  much  sugar,  at  4,  5  and  9  cents  a  pound,  must 
be  mixed  with  72  pounds  at  12  cents  a  pound,  so  that  the 
mixture  may  be  worth  8  cents  a  pound  1 

248.  Insert  four  arithmetical  means  between  2  and  79. 

249.  A  person  wishes  to  discharge  a  debt  of  $1125  in  18 
annual  payments,  which  shall  increase  in  arithmetical  pro- 
gression. How  much  must  his  first  payment  be  in  order  that 
the  last  may  be  1201 

250.  Three  merchants  have  an  interest  in  a  steam  vessel ; 
A  puts  in  $960  for  six  months ;  B,  a  sum  unknown,  for  12 
months ;  C,  $640  for  a  time  not  known  when  the  accounts 
were  settled;  A  received  $1200  for  his  share,  stock  and 
profit;  B,  $2400  for  his,  and  C,  $1040  for  his.  What  was 
B's  stock,  and  C's  time? 

251.  In  the  foregoing  question  A's  gain  was  $240  during 
6  months  ;  B's,  $800  during  12  months,  and  C's,  $400  during 
15  months,  and  the  sum  of  the  products  of  their  stocks  and 
times  was  34560.     What  were  their  stocks  1 

252.  In  the  same  question  the  sum  of  the  stocks  is  $3200 ; 
A's  stock  was  in  trade  6  months;  B's,  12  months,  and  C's,  15 
months ;  at  the  settling  of  accounts,  A  is  paid  $240  of  the 
gain ;  B,  $800,  and  C,  $400.     What  was  each  person's  stock  ? 

253.  A  man  bought  a  piece  of  property  for  $10500,  and 
agreed  to  pay  principal  and  interest  in  3  equal  annual  install- 
ments.    How  much  was  the  annual  payment,  interest  being 


^NST^ERS. 


Ex.  I  Answees. 

1  $34420.30. 

2l$1101.82. 
3 '$130200. 
4 '$3917660937.40. 
5 '$4.35. 
6  $94353.54. 
7 1 69 1904  acres. 
8 1 $24574740. 
9 1 7710. 
10 1 476  vessels. 

11  $1443394.34. 

12  $115.77. 

13  23171  mi. 

14  10051  mi. 


2535  mi. 

$14250. 

2358162. 

105. 

Loss  6742;  Strength, 

28888. 
3135283. 
Length,  2098  mi. 

Cost,  $115555000. 
863035  volumes. 
365795  more  vol.  in 

Mass. 
53  scholars. 
$7000. 
29300      charts      and 

maps. 
480. 

$2206080000. 
$3.06. 
66880000  Acres. 

104500  sq.  mi. 


p. 

Ex. 

23 

30 

a 

31 

u 

32 

(( 

33 

(( 

34 

u 

35 

(; 

36 

24 

37 

(( 

38 

u 

39 

(i 

40 

<( 

41 

« 

42 

u 

43 

25 

44 

u 

45  1 

(( 

46; 

(( 

47  j 

(( 

48 

(( 

49! 

11 

50 

u 

51 

26 

52 

(( 

53 

(( 

54 

u 

55 

(; 

56 

li 

57 

ANSWEEa. 

$12772.81. 

$19294. 

No.    of   stamps    96- 

847073. 
Value   of   the   same, 

$3676218.52. 
$101.72. 

30  representatives. 
36. 

318  men. 
17  mi. 
No.    of   pieces,    880- 

896255. 
Value.    $889635497.- 

32. 
$220. 

63678  sq.  mi. 
140320  men. 
Gain    $6    per    head. 

Bought  220. 
67702280  bu. 
$126. 

3  times  greater. 
524  banks. 
47  33191  men. 
$711000. 
31017921. 
23110  vol.^ 
8  years. 
32  boxes. 
6200  schoolhouses. 
$81016. 
6670. 

$16548531. 
$3923373. 


190 


ANSWERS. 


Ex. 

58 
59 
60 
61 
62 
63 
64 
65 

67 

68 
69 

70 

71 

72 
73 

74 
75 
76 


78 


79 


80 
81 

82 
83 

84 
85 
86 
87 
88 


Answee. 

158524335. 

$3.23. 

2736  years. 

$116000. 

$460. 

$350. 

$5656705.49. 

$1099262.78. 

$2444628.14. 

$1086600. 

20213  men. 

139180. 


A,  5;  B,  9, 


and  C, 


12. 

60  males,  207  fe- 
males. 

$888082128. 

$895796630.98. 

$5329044.02. 

$37424.99. 

No.  of  pieces,  186- 
502. 

Value  $3184892. 

No.  of  pieces,  1076- 
900. 

Value,  $358217.80. 

No.  of  pieces,  895- 
923. 

Value,  $17510960. 

No.  of  pieces,  1976- 
250. 

Value,  $815875. 

$24688477.12. 

$400. 

$21^680355.50. 

Greater,  1520;  less, 
967. 

$359312.63. 

21  hours. 

3750  lb. 

970  men. 

128  men. 

476. 


p. 

30 


Ex. 

90 


31 

91 

u 

92 

u 

93 

(( 

94 

a 

95 

(( 

96 

a 

97 

u 

98 

a 

99 

32 

100 

(( 

101 

a 

102 

li 

103 

a 

104 

u 

105 

u 

106 

u 

107 

u 

108 

u 

109 

u 

110 

a 

111 

a 

112 

u 

113 

a 

114 

ii. 

115 

ANSWEXt. 

1st  year,  626  ;   2d, 
676;     3d,  726; 

4th,  776  pairs. 
$827270.38. 
Jan.    1,    1863,   $1- 

472000. 
Jan.    1,    1864,  $2- 

422000. 
462  lb. 
$18. 

727038    more    fe- 
males. 
425. 
$93.87-]. 
3. 

62000. 
$62. 

3015  men. 
Average  value,  $4- 

000. 
Average  No.  acres, 

80. 
10  of  each. 
4720  prisoners. 
225,  or  75  of  each 

kind. 
1517706. 
A,  $1350;  B,  $2- 

250 ;    C,  $1440 ; 

D,  $2160. 
$150417.25. 
25  men. 
5500  killed,  21000 

wounded,  and  13- 

621  prisoners. 
785  yd. ;   gain,  $5 

per  yd. 
$6. 

23849. 
Steamboat,  15  cts.; 

coaches,  24  cts. ; 

railroad,  11  cts. 
2834  killed;  13709 


ANSWERS. 

lyi 

Ex. 

Answee. 

p. 

Ex.                   Answxb. 

wounded ;  and  6- 

37 

146  $78^5102. 

643  prisoners. 

(( 

147  $1144868.27. 

116 

109  bu. 

(• 

148 

10  cents. 

117 

595997. 

u 

149 

96  tons. 

118 

95864. 

38 

150 

37500  rations. 

119 

30  oxen;  10  horses. 

u 

151 

8179  persons. 

120 

7962032  sq.  mi. 

li 

152 

$2310000. 

121 

$22  per  hlid. ;    H 
gain. 

u 

153 

One,   13  mi.  ;    the 

other,  7  mi. 

122 

1644  killed;   9262 

ii 

154 

43534245. 

wounded;  and4- 

u 

155 

1st,      $960 ;      2d, 

945  missing. 

$640;  3d,  $320. 

123 

$12340. 

li 

156 

6782. 

124 

13659  pensioners. 

Sum  paid,  $1227- 
643. 

39 

157 

Killed,  545 ;  wound- 
ed, 3688;  miss- 
ing, 303. 

125 

20  cents. 

u 

158 

Fore    wheels,    31- 

126 

$82.11. 

680;  hind  wheels, 

127 

$5000. 

22176. 

128 

430042. 

u 

159 

5  of  each. 

129 

383717. 

u 

160 

$533.01. 

130 

183855. 

(( 

161 

$43.66. 

131 

Those  who  left,  20 
bu. ;   the  others, 

40 

162 

120  mi. ;  meet  in  6 
hours. 

70  bu. 

(i. 

163 

$1354300. 

132 

Lost,  $1265. 

(( 

164 

360. 

133 

$1895643. 

u 

165 

Vessels,  161 ;  guns, 

134 

$11470. 

1175  ;    tonnage, 

135 

Pensioners,  1132. 

127931. 

Amt.    paid,    $143- 

u 

166  212138570. 

527. 

u 

167  36. 

136 

15  barrels. 

li 

168  49  cents  less. 

137 

$90450000. 

<; 

169 

745452. 

138 

75148690. 

(; 

170 

A  owes  B  7i  cents. 

139 

640  sheep. 

41 

171 1 20  melodeons. 

140 

138  years. 

a 

172 1 $906250000. 

141 

$13.20. 

u 

173  j  41000. 

142 

$1530. 

u 

174!lo00  votes. 

143 

4022  bu. 

c( 

175 

$961.50. 

144 

No.  of  stamps,  251- 

307105. 
Value,  $7078188. 

u 

176 

32  vessels  of  15985 
tonnage,  and  166 
guns. 

145 

$5884. 

li 

177 

$34309600. 

192 


ANSWERS. 


Ex. 
178 
179 
180 
181 
182 
183 
184 
185 
186 
187 
188 
189 
190 

191 
192 
193 
194 
195 
196 
197 
198 

199 

200 


Answeb. 

74.   , 

800  and  200. 

$25.95. 

126742019. 

1877620  letters. 

$212607.36. 

1622241.04. 

76. 

7  school-houses. 

$2.10. 

2076  men. 

$1078432. 

9  classes  of  ladies, 

8  of  gentlemen. 
$9977784.50. 
Oats,  90;  corn,  11.25. 
$6797420. 
6145821  letters. 
$122433.75. 
2557  men. 
5000  men. 
One,     187562  ;      the 

other,  288641. 
Cost,    $190;     sellmg 

price,  $175. 
21  yd.  each. 


CHAI^TER  III. 


1 

2 
3 
4 

5 

6 

7 

8 

9 

10 

11 

12 

13 


$9.10. 

2  5 

56.25  yd.  in  length. 
No.  of  scholars,  84. 

No.  unoc.  desks,  24. 
1001. 

$6. 
$25. 

Qf^  bbl. 
31il. 


j\  of  a  day. 

$5.50. 

$1597.36|. 


p. 

r.::. 

46 

14 

u 

15 

ii 

16 

u 

17 

u 

18 

(( 

19 

u 

20 

46 

21 

47 

22 

a 

23 

a 

24 

u 

25 

a 

26 

a 

27 

u 

28 

a 

29 

(( 

30 

<; 

31 

u 

32 

48 

33 

a 

34 

a 

35 

a 

36 

a 

37 

ii 

38 

u 

39 

li 

40 

<( 

41 

u 

42 

ii 

43 

a 

44 

ii 

45 

49 

46 

(( 

471 

a 

48 

a 

49 

a 

50 

ii 

51 

a 

52 

Answee. 

12734  car  loads. 
60  mi.,  1550  feet. 
A,   $2656; 
B,  $3414f. 

84  times. 

"l  0  5* 

$15.82i§. 

200  at  2  cents  each. 

150  at  3     " 

Ii  days. 

161. 

2541212537.5. 

31  cents. 

f  I  of  a  day. 

10  horses. 

.9999998. 

.75. 

$29692. 

2y9g  pounds. 

30  bu. 

$456. 

_7_ 
I  I  • 

65. 

30  yd. 

13]   lb.   butter,   12 

dozen  eggs. 
$50. 

$228.66f. 
86000. 
$188.64. 
133.3322  acres. 
$261.75. 
.2679745. 
27  pairs. 
$48,775. 
$5400. 
71  days. 
.574751. 
4320544.8215. 
ft  and  ^. 

P       T)  9    .     D     1  9 
■^'  Tft4  5    ^'  77" 

X,  $2250;   Y,  $14- 
250. 


ANSWERS. 


193 


p. 

Ex. 

49 

53 

li 

54 

50 

55 

<( 

56 

li 

57 

a 

58 

" 

59 

« 

60 

(( 

61 

ii 

62 

11 

63 

ii 

64 

51 

65 

li 

66 

li 

67 

<: 

68 

u 

69 

li 

70 

(( 

71 

ti 

72 

ti 

73 

52 

74 

u 

75 

(; 

76 

(( 

77 

a 

78 

u 

791 

a 

80 

-  81 

<( 

821 

B,  59 


75  of  one  party,  102 
of  the  other. 

A,  821 :  B,  823 ;  C, 

$25 ;  D,  827. 
82050900.67. 
1 

8700. 

83448318.50. 

191300070000000. 

82.94A-. 

1249.0259107. 

817.67^5. 

Value  of  the  rem. 
812.721^  ;  Gain 
on  the  whole, 
$20.561 . 

81.661. 

3.V- 
150  ft. 

A,  74  mi. 

mi. 

85.20. 

1 

T*2       7       421     3 
T3'   TT'   43  1?   8' 

157^  days;  A,  35 
times ;  B,  18 
times  ;  C,  20 
times. 

76116.48  strokes. 

51975  times. 

Enumeration,  82- 
853. 

Enrollment,  120- 
322. 

Attendance,  82476. 

851.50. 

160  sheep. 

57  1b. 

8224. 

John,  16;  James,  28. 

7  yd. 

$1226;64. 


p. 
52 
53 


54 


55 

li 
it 


Ex.  j  Answeb. 

83  41  Iff  mi. 

84150. 

S5' 8145.50. 

8G  8250. 

87  834.03|. 

83 

89 

90 

91 

92 

93 

94 

95 

96 

97 

98 


1711  bu, 
821 1. 

lOy^^  cents, 
21  bu. 
I  of  a  bu. 
85i. 

28.365  tons. 
826.25. 
51  men. 

3 

'21U 


mi. 
99j39|yd. 
100  154. 
101:882.875. 
102  8550. 
103,11  of  a  day. 
104  lOJiyd. 
105 1  Ui- 

106  190806     men     on 
duty. 
14363  men  in  hos- 
pital. 
2917  men  in  con- 
finement. 
14110  men  on  fur- 


107 
108 
109 
110 


111 
112 
113 


total 


lough. 
223776 

strength. 
U  of  a  yd. 

810570. 
Horse,  8116|. 
Saddle,  8331. 
8103^3. 

^ '  times  larger. 


Buggy, 


49^  days. 
7  d'ays. 


IM 


p. 
55 


56 


Ex. 

114 


115 
116 
117 

118 
119 
120 
121 

122 
123 

124 


u 

125 

57 

126 

(( 

127 

(( 

128 

(( 

129 

(; 

130 

(( 

131 

a 

132 

<u 

133 

a 

134 

« 

135 

(C 

136 

C( 

137 

58 

138 

ii. 

139 

(.(. 

140 

a 

141 

142 
143 
144 
145 


Answei?. 

p. 

Ex. 

Answer. 

Buchanan,  1839642 

58 

146 

A,  $360;  B,$270; 

votes. 

0,  $240. 

Fremont,  1342069 

59 

147 

$158,121. 

votes. 

Li 

148 

$1479.  ^ 

Fillmore,  874760. 

a 

149 

40  1b. 

931  bu. 

u 

150 

18  cents. 

5fy  days. 

u 

151 

Denmark,       1600- 

729  yL       bu.      for 

551  ;     Hoi  stein, 

$465-|i. 

544419;  Schles- 

$3.69. 

wig,  409900. 

6  acres. 

a 

152 

$.53 +  15  lbs.  nails. 

$13.95. 

u 

153 

3^3_  days. 

iyd. 

a 

154 

775iclu0(J0' 

41  f  hours. 

a 

155 

.0425. 

$6846-. 

u 

156 

60  ft. 

1 

44' 

a 

157 

$12. 

B,62|bu.;  C,41| 

60 

158 

No.  of  pieces,  211- 

bu.;  D,10j\.bu. 

788518. 

lif  days. 

Value,   $5908522.- 

14 1  doz. 

60. 

7i  oz. 

(( 

159 

10  days. 

$2828.51. 

a 

160 

Graduates,  60 ; 

17. 

males, 

4  times. 

u 

161 

$34.77. 

280  pupils. 

a 

162 

Horse,  $140 ;  No. 

$36.57. 

of  tickets,  40. 

Boy,   $713;    Girl, 

u 

163 

9  hours. 

$55|. 

a 

164 

1,  2,  4,  5,  7,  8,  10, 

12|f  days. 

14,    16,  20,  28, 

A,  $825  ;B,  $1650. 

35,   40,  56,  70, 

C,  $2475 ;    D,  $3- 

80,     112,     140, 

300. 

280,  560. 

$1141983.22. 

a 

165 

$700. 

37§  mi. 

61 

166 

$21518200. 

40081  yd. 

(( 

167 

128  gallons. 

5  times. 

I'. 

168 

36  years. 

Cow,  3A  mo,;  horse, 

a 

169 

$210841. 

2|  nio. 

u 

170 

$107359.36. 

$.90. 

(i 

171 

$1379.84. 

$13285. 

u 

172 

333  times  nearly. 

23190  men. 

u 

173 

47  jg  ounces. 

Slate,     25     cents; 

62 

174 

49.995045. 

book,  45  cents. 

a 

175 

$203.59. 

ANSWERS. 

195 

Ex 

Ans-web. 

p.  .  Ex. 

AXSWEB. 

176 

300  oranges. 

65 

206 

12|  hours. 

177 

^.30. 

a 

207 

825f. 

178 

Exterior  ring,  10573 

a 

208 

5  times. 

mi. 

a 

209 

81.40. 

Interior  ring,  17176. 

66 

210 

17  tons. 

179 

A,  3d.;    B.  4d.;    C, 

a 

211 

82231.93]. 

6  d.     All  together, 

u 

212 

Accidents,  99 ;  killed, 

lid. 

264. 

180 

8800.92- 

u 

213 

243  chestnuts. 

181 

Failed,    39 ;     admit- 

(( 

214 

22326224  bushels. 

ted,  154. 

u 

215 

288. 

182 

8130. 

u 

216 

tt'y  of  the  cost. 

183 

$300  each. 

u 

217 

A,  56  d. ;    B,  84  d. ; 

184 

11402382 gal.;  value, 

C,  126d.;  D,252d. 

83524847. 

67 

218 

3.03203125  times. 

185 

8210. 

(; 

219 

8139708.80. 

186 

A,  836;  B,  852. 

u 

220 

9yY  tons  of  coal. 

187 

Greatest,96851760mi. 

li 

221 

16  yd. 

Least,  93148240  mi. 

« 

222 

16560  rails. 

188 

1488.375  gal. 

(( 

223 

Brick,  996;    framed, 

189 

B.8170;  C,  81562. 

9970;    stone,  578; 

190 

120  bu. 

log,  216. 

191 

Nu.20027300 ;  value, 

(( 

224 

48. 

887109.60. 

(C 

225 

87350. 

192 
193 

780-  672.  286.  1  89-  21  0 

u 

226 

No.  of  lb.,  100;  cost, 
8.26. 

Bin2lh!rcin3,-''5h. 

194 

Killed,  1644;  wound- 

68 

227 

2  times. 

ed,  9272 ;   missing, 

a 

228 

1939322  letters. 

4945. 

it 

229 

8383851.62. 

195 

125  bu. 

u 

230 

6  days. 

196 

B,  41.075  acres;    C, 

(( 

231 

Hi  cents. 

20.825  acres. 

u 

232 

379.5  mi. 

197 

8541.50. 

u 

233 

22  and  14. 

198 

4bu. 

u 

234 

830. 

199 

ff|. 

69 

235 

20  days. 

200 

John,  5  ;    Henry,  7  ; 

u 

236 

.28  nearlv. 

Charles,  9. 

(C 

237 

57|  lb.  of  tea.     Cof- 

201 

S106||i. 

fee  8.45  per  lb. 

202 

8.213. 

(i 

238 

120  ft. 

203 

One    46.55   mi.,    the 

u 

239 

8|  mi. 

other,  38.125  mi. 

u 

240 

82. 

204 

10|  bu. 

(( 

241 

21111. 

205 

823563.86. 

u 

242 

7  mi. 

196 


ANSWERS. 


P. 
69 
70 


71 


72 


73 


Ex.  I  Answek. 

243  10  mi. 

244  Todays. 

245  470232  children. 

246  j^  of  a  day. 

247  860   A.   at   $13   per 

acre. 

248  1260  times. 

249  16   in   gold,  $.43  in 

frac.  cur. 

250  60  rd.  in  advance. 
I  Fox  ran  140  rd. 

251 1 11130  school-houses. 
2  6Uda. 

253  127  and  a  rem., 
I     ^7777.50. 

254  1 50  cents. 

255' A,  S8100;  B,  $6400. 

256 '  50-cent-pieces,  6  ;  25- 
I  cont-pieces,  24;  and 
I  25  of  each  of  the 
I      other^!. 

257  80970.836.  lb. 

258  Area,  937398  sq.  mi. 
i  Population,  237406- 
I  801. 

259ilri^ 

260  j  4 1-^  rd. 

261  A,  $480;  B,  $240; 

C,  8160;  D,  $100. 

262  18  da. 

263 1  '1:^307^863.50. 
264' 160  da. 
265!  $1396508.08. 


266 

267 

268 

269 
270 
271 

272 


Fortune,  $11900; 
gain,  $2350. 

$416.70. 

Saddle,  $40;  horse, 
$80. 

1556244390  acres. 

$6897239190. 

321  yd. 

Brandy,  94  gal. ;  wa- 
ter, 26  gal. 


p.  I  Ex 

731273 

''  ,  274 

"    275 

"  j276 

74 1 277 


278 
279 

280 
281 
282 

283 
284 
285 
286 
287 


288 
289 
290 

291 


76 


292 


Aksweb. 

$35379. 

$.271. 

1068779  men. 
$360,  $160,  and  $150. 
72   sheep;    687^  lb. 

butter. 
$1,671. 
$17000000. 
2751.5- 
97i  A. 
Dome,   143628;    In- 

dia,  75899. 
240  peaches. 
80  and  84  ft. 
01303304.50. 
e42.25. 
Whole   amt.,  53.767 

acres. 
One  part,  21.5068  A., 

the  other,  32.2602 

acres. 

2254552 

5:^- ore-*    , 

$121.05. 

Average  No.  62 ;  ex- 
pense, $12.35— 

30  min.  1st  horse, 
4500 rd.;  2d  horse, 
3600  rd. ;  3d  horse, 
£000  rd. 

Wheat,  $1.66|;  corn, 
$1;  whole  cost,  $20 


CHAPTER   IV. 

2 1  $2471.40. 

3  $14971316.72. 

2  A.,  6  P.,  15sq.  yd., 
TS  sq.  ft. 

230. 


34560  steps. 
16  m.  12  sec. 


p. 

Es.  1 

77 

8! 

(( 

9! 

" 

lOl 

" 

11' 

(( 

12' 

<; 

13. 

ti 

14 

^ 

u 

15 

78 

16 

<: 

17 

(( 

18 

{( 

19 

(( 

20 

« 

21 

( 

22 

(C 

23 

79 

24 

a 

25 

li 

26 

ti 

27 

(( 

28 

(( 

29 

(( 

30, 

(( 

31 

(( 

32 

ii 

oo 

.JO| 

BO 

34 

u 

35  i 

u 

36 1 

a 

371 

Akswek. 

i     P- 

J. 
•Ex. 

J-i7# 

1                          AXSAVEE. 

^'^-  . 

80 

38 

li 

19gal.  Iqt.  Ipt.y-^sgi. 

a 

39 

8175.86 +gain. 

%7. 

a 

40 

8182965.32. 

$5958.91. 

a 

41 

8100. 

$14.54yV 

81 

42 

239  mi.  3  fur.  22  rd. 

28000. 

5  yd.  4  in. 

Time,71i.44m.35ilf 

u 

43 

32  men,  each   3  fur.  2 

sec. ;  dis.  from  Alb., 

rd.  12|f  ft. 

168l|fi;     dis.   from 

8  men,  each  2  fur.  18 

Bufr.;i293-Z-^  mi. 
163530.40. 

rd.  3/^  ft. 

ii 

44 

Bra  mlette,68306  votes, 

Editor,  1;  lawyers,  6; 

AYickliffe,  17389  " 

merchants,  25;    far- 

u 

45 

£92  18s.  9d.  3e|  far. 

mers,    42 ;     clergy- 

u 

46 

A,  1723^  mi.;  6,15638^ 

men,  8. 

mi. 

10  cents. 

u 

47 

826.58|. 

81.121. 

a 

48 

13  C,  68 3L  cu.  ft. 

83625: 

(( 

49 

Rye,    81.15;    barley, 

88  bu.  4  qt. 

81.00. 

39  A.  3  R.  18  P.  0 

a 

50 

3  R.  7f  P. 

sq.  yd.  6  sq.  ft.   64 

82 

51 

Horse,  8150;  carriage. 

sq.  in. 

8600. 

292  mi.  5  fur.  16  rd. 

(( 

52 

9  mi.  7  fur.  8  rd. 

5  yd.  1  ft. 

a 

53 

819920767. 

18  da.  5  h.  11  min.  6| 

u 

54 

831  lb. 

sec. 

" 

55 

1092.728  mi. 

824031.25. 

u 

56 

1st,  29121;  2d,  22597; 

1 
35. 

Sd,  19383. 

1428  solid  ft. 

u 

57 

213.1  acres. 

190?  sq.  yd. 

ii 

58 

mmj.            . 

3  h.  15  m.  P.  M. 

ii 

59 

Primary,   1683;    Int., 

60,  at  1  a  cent  each. 

1275;    Gr.    School, 

90,  at  3  for  2  cents. 

459 ;    High  School, 

N.    J.    farmer    gained 

135. 

18l|  bu.  of  oats, 

83 

60 

Mixed,    81020;     Pri., 

worth  87.40p. 

86311.25;   Int.,  87- 

8143.55- 

968.75;  Gr.,  84781.- 

8.80. 

25 ;     High    School, 

81238.171. 

83281.25. 

111.  tons. 

u 

61 

90°  24'  W.  Lon. 

8448  years. 

i( 

62 

88.281.  ■ 

8520553.91. 

i( 

63 

9.2640625  A. 

816.67. 

19 

8 

ANSWERS. 

p. 

Ex.  1                   Answee. 

p. 

Ex.  1                 Answeb. 

83 

64 

Coinage,  116680;  dep., 

817594. 

87 

100 

Killed  and  prisoners 
each,  3500. 

u 

65 

11.00. 

Wounded,  16400. 

ii 

m 

81260. 

(( 

101 

56.25,  and  43.75. 

u 

67 

Lincoln,  1866452. 

(( 

102 

87.957  + 

Douglas,  1375157. 

(( 

103 

$12.50/:.. 

Breckinridge,  847953. 

(( 

104 

£408  17s.  9M. 

Bell,  590631. 

il 

105 

21b. 

84 

68 

.0065  of  a  ton. 

88 

106 

8357  spent  unneces- 

a 

69 

408883200  mi. 

sarily. 

li 

70 

1186888.25. 

1138  books. 

(( 

71 

19i  bunches. 

(( 

107 

8950.36  + 

li 

72 

141.25-bu. 

(( 

108 

$75,831. 

a 

73 

8 h.  59m. 20 sec.  A.M. 

(( 

109 

$204.75. 

a 

74 

27 y\  min.  past  8. 

u 

110 

197.325. 

li 

75 

I20.09i|. 

(( 

111 

$2010.52^. 

(( 

76 

88  P.  97  sq.  ft.  12  sq. 
in. 

u 

112 

4   d.   10  h.  34  min. 

38  sec. 

li 

77 

$660000. 

li 

113 

829741.25. 

85 

78 

$395,921. 

89 

114 

98.8  acres. 

u 

79 

31  yr.  2  mo.  20  da. 

a 

115 

6|. 

li 

80 

1220. 

a 

116 

893.86|. 

li 

81 

$7.90. 

a 

117 

81788.15. 

il 

82 

38°  44'  18.75". 

il 

118 

51    bags  ;     capacity, 

li 

83 

$1231. 

m  bu. 

li 

84 

82.625. 

a 

119 

$.70. 

86 

85 

$1.25. 

il 

120 

8. 

(4 

86 

172  d.  20  h.  47  min. 

a 

121 

8540425. 

49 1  sec. 

90 

122 

23328  bricks. 

U 

87 

$907946.56. 

u 

123 

£40  Os.  2d. 

(( 

88 

8519.531. 

li 

124 

£734  8s.  Id. 

u 

89 

10s.  6d. 

li 

125 

81330424.24. 

u 

90 

$6.74. 

u 

126 

8102521.60. 

u 

91 

m- 

(( 

127 

8133.42. 

u 

92 

15. 

(( 

128 

8390. 

a 

93 

526|  sq.  yd. 

(( 

1291811.25  and  $8.75. 

li 

94 

149   lb.    5  oz.  1.19- 

91 

130 1 

dr. 

a 

131 

30   d.   23  h.   25  m. 

li 

95 

18  oz. 

26|  sec. 

87 

96 

608025971 1  gal. 

C( 

132 

8.831. 

i; 

97 

823  831. 

(( 

133 

825.20. 

a 

98 

lft6,V8'9in- 

(( 

134 

82.00;  18  1b. 

(( 

99 

12666  men. 

u 

135 

5  ft.  2§  in. 

p. 
91 

(( 


92 


u 
ii 

93 

a 
(( 

(C 

II 

u 


94 


95 


ANSWERS. 

lyy 

Ex. 

136 

Answeb. 

84  yr.  9  m.  8  d. 

p. 
95 

Ex. 

167 

Anbweh. 

•2  ft.  Slii  in. 

137 

8139. 

a 

168 

leiiAV 

138 

SI 699932053. 

a 

169 

5. 

139 

11880  bu. 

a 

170 

85967  francs. 

140 

1.0083  were  sold. 
54.116  remained. 

u 

171 
172 
173 

$602.25. 

fV,  tVt,  1^.  and  W- 
97845  men. 

141 

1026864000. 

a 

174 

87164  men. 

142 

.^210.50. 

96 

175 

100  iral 

143 

$15.36i. 

(( 

176 

$72L40. 

144 

^7.07 -f 

a 

177 

Sound   after    flash, 

145 

30  gal. 

^mnm  ^^c. 

146 

261252  persons. 

Ball  after  sound, 

147; 

S5.60  + 

lU4||sec. 

148 

8  A.  3  R.  301  P. 

(( 

178 

4h.  8  m.  36i  sec. 

149 

S33.5S|. 

a 

179 

$26H. 

150 

32148. 

a 

180 

28  T.  14  cwt.  21  lb. 

151 

,37  bells,  and  6577  lb. 

14  oz. 

remaining. 

u 

181 

Debt,     $133.56-In- 

152 

88  mi.  2  fur.  2  rd. 

terest,  $4.35  4- 

153 

2x2x2x5x5x7. 

u 

182 

Debt,  $61.28-Inter- 

154 

24. 

est,  $3.05. 

155 
156 

$354. 

17  mi.  28  rd.  12  ft. 

183 
184 

$11665.72. 

4 

157 

47T  in. 
13423  mi.  2  fur.  14 

(( 

185 

Copper,  289287  lb. 
Tin,  96429  lb. 

rd.  9  ft. 

97 

186 

One,  $5.45f  J  ;  other, 

158 

July     14,    1858,    at 

$8.1 8yV 

noon. 

" 

187 

14i|  bu. 

159 

$32.04i. 

a 

188 

108  steps. 

160 

11  Si  cu.  ft.  each  load. 

u 

189 

6. 

Price  per  cord. 

u 

190 

$443,061. 

$4,263. 

u 

191 

1308  ft.  2'  8". 

161 

£3215  2s.  5|d. 

a 

192 

124  ft. 

162 

$21588.90. 

a 

193 

148  cu.  ft.  0'  4". 

163 

108. 

a 

194 

23779  animals  for 

164 

Corn,   28011  g?   bu.; 

$592758.25. 

wheat,27imjbu.; 

u 

195 

$704.70. 

rye,  604,%\  bu. ; 

98 

196 

$.70. 

money,    $1089.66- 

u 

197 

2  A.  1  R.  18  P. 

2  83  4 
4  3  0  1* 

ii 

198 

$206819597.20. 

165 
►  16C 

25  rd. 
>!l  mi.  20G0  ft.  8  in. 

a 

199 

?. 

200 


ANSWERS. 


Ex 
200 

201 

202 

203 
204 

205 

20C) 

207 

208 
209 
210 


211 


212 
213 
214 


215 
216 

217 
218 
219 
220 
221 
222 
223 
224 
225 
226 
227 

228 

229 


Answeb. 

Iw.  4d.  14h.  50 m. 
51  sec. 

$4.60. 

2228560 mi.;  89^^^^ 

times. 
86°  21'  W.  long. 
$432,941 
$348.80  + 
167  and  7. 
6  oxen,  30  cows,  210 

sheep. 
20  A.  3  E.  91  P. 
707  hhd.  57f  gal. 
22  gi]],  44  half-pint, 

8^8  pint,  and  176 

quart  bottles. 
Marriage,    Dec.   30, 

1857. 
Child's     birthday,  - 

Jan.  20,  1861. 
$35.86  + 
6616746  bii. 
Sold  $2,621.    One's 

gain,   $.171;    the 

other's  gain'J  $.261. 
3  h.  40  min.  52  sec. 
4y^3    min.    before 

twelve. 
$.17|i. 
$60i|. 
$48182005. 
16  min.  21j\  sec. 
8f\  min. 
240  bu. 
$2,663-. 
21|  gal. 
$4336884. 

Man,  21  mi. ;  Boy  2 

mi. 
15  T.  12  cwt.  811 

lb. 
$3.72 +  $3.05,  $8.20. 


p. 

Ex. 

102 

230 

(( 

231 

" 

232 

a 

233 

u 

234 

a 

235 

a 

236 

u 

237 

u 

238 

103 

230 

a 

240 

u 

241 

u 

242 

u 

243 

a 

244 

a 

245 

a 

246 

u 

247 

a 

248 

104 

249 

" 

250 

(( 

251 

({ 

252 

a 

253 

a 

254 

a 

255 

li 

256 

li 

257 

u 

258 

105 

259 

(( 

260 

(( 

261 1 

u 

2621 

u 

263 

u 

264 

Anbweb. 

Killed,  890 ;  wound- 
ed, 3627 ;  prison- 
ers, 1222. 

$12. 

7. 

1  lb.  51  oz. 
80  ft. 

28°  35.06'. 
16578  school-houses. 
7306  libraries. 
Passed  ex.  20096. 
Rejected,  7010. 
Chain,  £6  13s.  4d. 
Pencil,  £3  6s.  8d. 
Watch,  £20. 
19  bu. 

2  cords. 

I  of  a  pound  of  each. 

_8_0_ 
J  8  9" 

$7.85y\. 

1st,  $4,393  ;  2d, 
$11,607;  3d,  $9.- 
85;  4th,  $1.42. 

1/7^  lb.  avoirdupois. 

$851  + 
21296  sq.  ft. 
y\  of  a  cord. 
4000  men. 

$150. 
485.1  bu. 

$5957.55- 

^H T  0  (5 0  ^^  ^^  i"^^* 

576. 

$1605.35. 
$71.59i|. 

4  0.  lf3.2f3.4Om. 
36  cents. 
$75. 

23  h.  18  m. 
181000. 


AlsSWERS. 

2Ui 

Ex.     1                         AK6WEB. 

P.        Ex. 

AssvrrB.. 

26516836408.13- 

108 

297 

25?  bu. 

266,4485  yd. 

a 

298 

1291734653  sec. 

267  .992  of  a  short  ton. 

u 

299 

350  A.  3  R.  37.12  P. 

268:10,\     hours,     and 

109 

300 

8569.82  + 

148|^  mi. 

a 

301 

14  ft.  2'. 

269  15  yd. 

(( 

302 

5  yr.  76  d.  i  h. 

270 

17-.,Vy  mi. 

u 

303 

2230272000  pigeons 

271 

252. 

a 

304 

448  yd.  2f^  cir. 

272 

89Jg  yd. 

a 

305 

lO/g  cords. 

273 

276.64  statute  mi. 

a 

306 

85.20. 

274 ;  5  pieces.                      | 

a 

307 

8618082.81. 

275 

4296  ft.  9'  8". 

n 

308 

82.58. 

276 

7f!.  2f3.  54n. 

a 

309 

81.401?. 

277 

178  mi.  5  fur.  8  rd. 

110 

310 

8.86- 

4  ft.  44  in. 

(; 

311 

1280785763  hhd. 

278 

A6.07- 

16f  gal. 

279  i  $2.12- 

(( 

312 

835891.89  + 

280 '8.57- 

a 

313 

21  f  pipes  of  Port. 

281  7  in. 

a 

314 

81148.29- 

282 

Eldest,   86478.83- 

a 

315 

8213.11- 

2d,    84859.12- 

u 

316 

1  to  everv  42|  nearly 

3d,    83644.34- 

a 

317 

Nitre,  1500  lb.,  sul- 

4th,  82733.25  + 

phur  and  charcoal, 

283 

85  verses. 

250  lb.  each. 

284 

Private,  lOi  acres  ;  j 
Sergeant,       20|  ; 

" 

318 

248832   cu.  quarter 
in. 

Lieut.,  6U;Capt., 

111 

319 

51°  25'. 

81 1;  Maj.,  1424; 

a 

320 

8114.40. 

Col.,  204  acres. 

a 

321 

8279.31^. 

285 

7  oz.  4  pwt.  16  gr. 

a 

322 

Can.  more  than  Mo., 

286 

872343. 

49200000. 

287 

631. 

Total,  1038800000. 

288 

Yy  ofahhd. 

a 

323 

10  h.   54  m.  44  sec. 

289 

8132.21- 

i 

P.  M.  of  the  pre- 

290 

llOi. 

vious  day. 

291 

23.17690625  mi. 

li 

324 

8734.1  U. 

292 

1216932. 

293 

33  bales. 

294 

8100.46|. 

295 

A,   8384.47;    B, 
8291.07;  C, 8221.- 

CHAPTER   V. 

89. 

112 

1 

8520. 

296 

85416- 

u 

2 

180  bu. 

202 


ANSWERS. 


Ex 


Anbwkb. 

1st  yr.  600  lb. 
2d    "     720  " 

$8.54+ 

$871278.29 

$723. 


204  o. 

Annual  int.  $2160477 

57  men. 

$1300. 

331^. 

17|  d. 

$43.75. 

$9.08J. 

Gain,  $20703| ;   rate 

of  gain,  4  J^. 
17  j  Cost,    $120;     asking 

price,  $150. 
Feb.  17,  1859. 
$21. 
25^. 

March  2d,  1864. 
3  wk.  3  d.  6  h. 
8|  cents. 
4A  yr. 
$2.00. 
Neither. 
$13720.05. 
Infantry,  525000. 
Cavalry,  100000. 
Artillery,  66000. 
Gens  d'armes,  26000. 
$169. 

3o'^  months. 
2825  bu. 

7's  at  105^,  by  j%fo. 
8^. 

$31801.82— 
$375X5. 
$1076995. 
14^  days. 
$1600. 


p. 

Ex 

116 

IS9 

a 

|40 

a 

41 

(( 

42 

117 

43 

(4 

44 

U 

45 

u 

46 

(( 

47 

ii 

48 

a 

49 

u 

50 

« 

51 

118 

52 

u 

53 

ii 

54 

il 

55 

ii 

56 

(( 

57 

u 

58 

ii 

59 

ii 

60 

119 

61 

u 

62 

ii 

63 

c; 

64 

u 

65 

;( 

66 

a 

67 

(( 

68 

a 

69 

u 

70 

120 

71 

" 

72 

1  « 

73 

times  as  great. 


AKSToat. 
120.82-^ 
457.94-^ 
1964- 
$407. 

4  oxen,  at    $50;    24 
cows,  at  $25  ;  and  72 
sheep,  at  $5. 
20-/. 
$42,875. 
$.033  on  $1 ;    S.  P. 

Norton's  tax, 

$511.86. 
12  men. 
$111,906  + 
$101.06+ 

6  per  cent. 

$2625. 
$46.75. 
$14350. 

n%- 

120  reams. 

$5702.23- 

75^  of  par  value. 

:H698.37  + 

457  mi.  3990  ft.  long. 

Time, 

$1920. 

Gained  $77.50. 

Lost,  $521.56. 

$21355.54. 

33^^. 

21  T.  5  cwt. 

$5.34. 

.0192- 

Wife   and  son,  $480 

each  ;    daughter, 

$360. 
101^. 
$5.05- 
$13.06- 
37587440. 
226  A.  1  R.  34  P. 


183  h.  Q^\  min. 


ANSWERS. 


203 


Ex 

74 
75 
76 

77 

78 


80 
81 

82 
83 
84 
85 

86 
87 
88 
89 
90 
91 
92 


93 


94 
95 
96 

97 
98 
99 
100 
101 
102 
103 

104 


Answhs. 

1200  barrels. 

8700. 

Sept.  4,  1860,   bal. 

due. 
A,  89000;  B,  $4800; 

C,  $7200. 
Gold,  9  pwt.  16i  gr. 
Silver    and    copper, 
12/y  gr.  each. 
$250. 

$59.40. 

$93.75. 

183732. 

Commission,  $1040. 

Net  proceeds,  $2820. 

$368.85  4- 

61  mi. 

$2500. 

$126.02  + 

8000  bu. 

$11377.77- 

New  York,  222856 ; 

Pa.,  200320 ;   III, 

135529;   Ohio, 

170272. 
Cost  of  sh.,  $2.75|. 

"      broadcloth, 

$17.91 1. 
$.93|. 
$84.63  + 
B's  stock,  $2800 ; 

C's  time,  9  mo. 
$.322- 
Gain,  $5.25. 
25  cwt.  2  qr.  10  lb. 
826163.265  + 
180  mi. 
1  /J^. 
A,$842.30;B,$918.- 

87;  C,  $1598.83. 
$5369.62- 


p. 

Ex. 

124 

105 

u 

lot) 

a 

107 

(C 

108 

u 

109 

ii 

110 

li 

111 

125 

112 

u 

113 

il 

114 

ii 

115 

u 

116 

a 

117 

a 

118 

u 

119 

126 

120 

a 

121 

a 

122 1 

a 

123! 

a 

124! 

li 

125 

il 

126 

127 

127 

;( 

128 

(( 

129 

u 

130 

(( 

131 

u 

132 

li 

133 

(( 

134 

" 

135 

Answeb. 

43iJ  yd. 

$5.50  per  yd. 

A,    $1000;    B,    $1- 

125;  C,  $875. 
$1177. 
$580.38. 
40200  men. 
$3.51- 

Males.  206367. 
Females,  18C713. 
$220.29  + 
21  years  old. 
265^. 

$187454.63. 
310. 
24  lb. 
Entire     profit,     $8- 

333.37. 
Due  from   Gwin  & 

Co.,  $21368. 
Paid  to  A,  $8127.- 

18A. 
Paid^to  B,  $8511.- 

431. 
$1456.52- 
12  d.  11  h.  29  m. 

29  + sec. 

Sfc. 

33.75  yd. 

$212.50. 

$178.63. 

912. 

3  yr.  2  mo. 

$.52— inHav;$.8.")3 
— in  store;  selling 
price,  $,,1,023  + 

251  lb. 

20|/. 

1061^  sq.ft. 

489S00  lb. 

$2.23. 

Oct.  19,  1864. 

331^. 


204 


ANSWERS. 

Ex.  I                Answeb. 

p.    !  Ex. 

Answib. 

136 

$43189600. 

132 

172 

128|  yr. 

137 

255^. 

a 

173 

$564.40- 

138 

10;!^. 

li 

174 

51  da. 

139 

$1003.12.1. 

u 

175 

$,30. 

140 

11  in. 

(( 

176 

81.25^. 

141 

181556. 

a 

177 

9|  oz. 

142 

A's,  8;  B's,  12; 

(( 

178 

£1. 

C's,  16  months. 

u 

179 

^5^. 

143 

13t\/^. 

133 

180 

$105.84. 

144 

68iC 

a 

181 

$390. 

145 

13i^. 

u 

182 

$865.45. 

146 

6000  privates,  100- 

u 

183 

$1.80. 

000  arms. 

u 

184 

$.971  + 

147 

36,  54,  90. 

u 

185 

$5970. 

148 

126. 

u 

186 

405  lb. 

149 

10;^  loss. 

(( 

187 

$161.94. 

150 

No  more. 

(( 

188 

$13000. 

151 

666900  mi. 

C( 

189 

51J^. 

152 

1124.10. 

<( 

190 

1386  sq.  ft. 

153 

13100000. 

(.1 

191 

39/3^. 

154 

$110. 

134 

192 

812.50. 

155 

$3264.21  + 

(( 

193 

$1.68. 

156 

5|  cents. 

n 

194 

$5591205.50. 

157 

Invoiced  value,  $.60 

ii 

195 

60^. 

per  yd. 

a 

196 

Aug.  15,  $27^99. 

Cost  after  duties,  etc. 

Jan.  1,  $142.01. 

$.85  per  yd. 

li 

197 

132  da. 

158 

12314  men. 

« 

198 

4f.'. 

159 

24  sacks. 

u 

199 

$1200. 

160 

$600. 

u 

200 

5.729  + gal. 

161 

$1000. 

135 

201 

2921. 

162 

12.308  acres  nearly. 

u 

202 

20000  men. 

163 

$.75. 

u 

203 

$5522. 

164 

3fV  mi. 

204 

$75  at  first.     A  had 

165 

17  h.  2f  min. 

(( 

$18;  B,  $32.25. 

166 

$240. 

u 

205 

$5165.12^.. 

167 

11.76-^ 

u 

206 

24  per  cent. 

168 

$8346.11. 

u 

207 

2m.5f.  12rd.  13  ft. 

169 

DueSept.2d|5th,148 

11 

208 

$1200. 

days  to  run. 

u 

209 

$253,132. 

Proceeds,  $561.43. 

(( 

210 

$.141. 

170 

24. 

136 

211 

Act.  in.,  $185712741. 

171 

16i^. 

In.  per  ct.  837.98  +  ^ 

. 

ANSWERS. 

205 

p. 

Ex. 

Answer, 

p. 

Ex 

AXBWEE. 

136 

212 

A's,$180;B's,$135; 

139 

245 

81513291042.35. 

C's,  8120. 

li 

246 

N.  Y.  loan,  822. 

u 

213 

83032.56- 

140 

247 

81274.074. 

u 

214 

3750. 

a 

248 

8318.81|. 

11 

215 

10|  mo. 

u 

249 

154  ft. 

li 

216 

Charleston,  loss,  5.6^ 

(( 

250 

8659645. 

New  Haven,gain  93^ 

ii 

251 

55|^. 

('. 

217 

9fo. 

u 

252 

A's,  8684;  B,  8912. 

ii 

218 

8250. 

ii 

253 

81.25  per  bu. 

li 

219 

840. 

(( 

254 

8990.75. 

ii 

220 

227  gal. 

(( 

255 

847.13- 

137 

221 

Capital,    82  ;      raw 

ii 

256 

8242347.93  + 

material,  81.90. 

*i 

257 

A's,8440;  B's,8480. 

Amount      produced 

141 

258 

1  A.  3  R. 

by  each,  8600. 

a 

259 

April  8,  1859. 

u 

222 

June  23,  1863. 

u 

260 

June  13,  and  Aug.  1. 

(; 

223 

81227.13. 

a 

261 

82120.63- 

u 

224 

Neither. 

(i 

262 

16^. 

(; 

225 

185f^. 

(( 

263 

843111600. 

(( 

226 

2  m.  lOJ  da. 

a 

264 

810.45  + 

(( 

227 

Capital,  ^8 1.444 

a 

265 

66lfo. 

nearly. 

a 

266 

812.00. 

Raw  material,81 .76— 

142 

267 

84497.75. 

Each  hd.,  8569.90 - 

ii 

268 

93/^^  nearly. 

138 

228 

13  bales. 

a 

269 

m^- 

(( 

229 

1000  doz. 

1.1. 

270 

3223^1. 

li 

230 

16  y.  8  mo. 

a 

271 

82.74- 

a 

231 

8120.      * 

ii 

272 

8151.25. 

a 

232 

Students,  836 ; 

Alumni,  7182. 
Vols ,  151620. 

a 

273 

Actual  increase, 
89023835840. 
Increase,    per    cent., 

(( 

233 

A,  8571 1;  B,428|. 

12646-,^ 

a 

234 

82040. 

a 

274 

82309.03- 

a 

235 

m  y^- 

ii 

275 

11  ft.  8  in. 

a 

236 

61800. 

li 

276 

8750.75. 

a 

237 

8_ 

ii 

277 

9  m.  20  d. 

139 

238 

85393.61|. 

143 

278 

8121.57. 

(( 

239 

8569. 

a 

279 

Bushels.  91350000. 

u 

240 

128.898-yr. 

Value,  816650000. 

(( 

241 

83.66- 

(( 

280 

87831.92. 

li 

242 

5^. 

a 

281:4,^. 

(( 

243 

830,  842,  848. 

a 

282i71°3' W.Long. 

(( 

244 

8494.80. 

•' 

283! 

810628564. 

206 


Ex. 

284 

285 
286 
287 
288 
289 
290 
291 

292 


293 
294 
295 

296 

297 
298 
299 
300 

301 
302 
803 
304 


305 


306 
307 
308 
309 
310 
311 1 

312: 
313 
314 
315 


ANSWERS. 

Answer. 

p. 

Ex. 

Answer. 

A,  20d.;   B,  24cl.; 

147 

316 

4i^;  total  loss,  4500. 

C,  30  d. ;  all,  8  d. 

a 

317 

2734. 

500  tons. 

a 

318 

7  cwt.  2  qr.  18+ lb. 

38743,9^3  yrs. 

" 

319 

6912. 

40  shares. 

u 

320 

25^. 

12030.50. 

u 

321 

$104. 

28981300. 

u 

322 

$8,654- 

100  bales. 

u 

323 

16§^. 

14018.24  bor.,  |62.- 

u 

324 

135. 

61  gain. 

148 

325 

50^. 

C's  stock,  $10000. 

u 

326 

$3808. 

A's  gain,  $336 ;  B's, 

u 

327 

10^^. 

1504. 

(( 

328 

Jones,    $6585  ; 

540. 

Brown,  $5535; 

1780. 

Hall,  $4482 ; 

Sheeting,  $.12i;  cali- 

Smith, $2853. 

co,  $.10. 

a 

329 

$125.10. 

150  fo. 

u 

330 

791^. 

64  mi.  1689|  fl. 

a 

331 

1 6 1  ^^  of  the  wounded. 

4  mi.  2645.5+ ft. 

lli^     "      whole 

$.30. 

loss. 

80    in.  long,   60  in. 

149 

332 

Killed,  1000; 

wide ;  32  in.  thick. 

Wounded,  6000. 

10  hom^s. 

Prisoners,  2000. 

B,  $60 ;   C,  $50. 

a 

333 

$4.75. 

$1104.80. 

(; 

334 

20  mi.  2  fur.  10  rd. 

A,    $39.i56|  ;      B, 

2|f  ft. 

$46.9871;  C,  $62.- 

u 

335 

525  hours. 

65;  D,$70.481|. 

u 

336 

1  gal.  2  qt.  1  pt. 

Inf.  10800,  art.  660. 

a 

337 

1st,  45;    2d,    145; 

Total  surrender,  11- 

3d,  275. 

583. 

a 

338 

Corn,  $1.50;  wheat, 

^%^ 

$1.75. 

A,  $588;  B,  $1078. 

a 

339 

A,  $260.42;   H, 

28^. 

$135.42;  M,$72.. 

ttI  mi. 

92;   K,  $31.25. 

$5000. 

u 

340 

33  min.  25^^860.  past 

8  hhd.  30  gal.  1  pt. 

midnight. 

1.7  gi. 

a 

341 

$3200. 

mj. 

c; 

342 

27. 

Feb.  4,  1860. 

150 

343 

$47224. 

$846. 

a 

344 

$1506/.. 

621,^. 

(( 

345 

$640.49e 

ANSWERS. 

207 

p. 

Ex 

Answer. 

p.    1  Ex. 

Anbweb. 

150 

346 

M,  $2750 ; 
N,  $2000. 

a 

384 

Direct,    $14224.91  ; 
circular,  $14476.- 

ti 

347 

$234,871. 

73;  gain,  $251.82. 

li 

348 

$6765. 

ii 

385 

^H%' 

li 

349 

5200  men. 

il 

386 

$2. 

u 

350 

416  mi. 

li 

387 

$166.66f. 

u 

351 

162. 

ii 

388 

$200. 

151 

352 

Hfo. 

155 

389 

$37.77- 

(( 

353 

2bfo. 

a 

390 

8  cents. 

(( 

354 

^n%- 

a 

391 

$14075000. 

(( 

355 

2bfc. 

a 

392 

$1683  worth  of  sugar. 

4; 

356 

$255. 

a 

393 

$3000  + 

u 

357 

$302.80- 

ii 

394 

$958.55. 

u 

358 

$846.25. 

u 

395 

$.387. 

(( 

359 

$1.07§J. 

u 

396 

sooooo. 

u 

360 

322. 

(( 

397 

$740. 

li 

361 

5  m.  4  d. 

156 

398 

84392000. 

u 

362 

$329.37. 

li 

399 

$5400. 

152 

363 

$18.90. 

a 

400 

Smith's,  $3500; 

u 

364 

$793403.48. 

Boise's,  $4900. 

u 

365 

$28000. 

11 

401 

$386.48. 

(( 

366 

$26.56. 

a 

402 

28  cents. 

u 

367 

4640. 

11 

403 

$486300. 

(( 

368 

$400. 

11 

404 

33. 

(( 

369 

$85272. 

157 

405 1 7  m.  15  d.;  rate,  105^ 

(( 

370 

A's,  $4156.25;  M's, 

$92281; 
S's,  $15215.62^. 

a 

406 

Firm,  $9150  ; 
Marks,  $3050 ; 
Willis,  $1830; 

153 

371 

5^. 

Sterrett,  $4270. 

a 

372 

$2237.646. 

u 

407 

216  rd.  2  yd. 

a 

373 

H- 

(( 

408 

$1376751. 

a 

374! $51 1824.                    1 

u 

409 

$2820. 

li 

375 

A's,  $4440 ; 

(( 

410 

81^;  J.  Smith,  $425. 

B's,  $4625 ; 

158 

411 

3346/3. 

C's,  $4810. 

a 

412 

$6666|. 

11 

376  Neither.                      | 

a 

413 

3|i^  discount. 

ii 

377 

$70.61 . 

a 

414 

6250. 

a 

378 

1  yr.  and  2  yrs. 

li 

415 

6  cents. 

154 

379 

$451690. 

11 

416 

2fo. 

(; 

380 

121^. 

u 

417 

$17480,  $14858, 

u 

381 

$88750. 

. 

$12920,  $12512. 

a 

382 

100  men. 

u 

418 

20000. 

a 

383 

$5010. 

(( 

419 

$.50. 

208 


ANSWERS. 


P. 
158 


159 


Ex. 

420 


421 
422 


423 
424 
425 
426 


Answee. 

Paris,    $14285.711; 

London,  $14600; 

Amsterdam,  $14- 

640. 
$54091.37  + 
Total  value,  $202 16- 

287. 
Rate     of     increase, 

181.8^. 
2^^  discount. 
$120. 
21  doz. 
$131756.15. 


sq., 


CHAPTER   VI 


3  ft.  2.72  in. 
$7435.56. 
12i  cents. 
Cir.    less     than 

$48.16. 
Sq.  less   than    Rect., 

$108. 
1st,    12^;    2d,    18^; 

3d,  30^. 
Length,  55.54  +  in.  ; 

bung  di.,44.43  +  in. 
2  y.  9  m.  15  d. 
$2.60,  $3.00. 
20  acres. 
232.457  rds. 
351b. 
20,  20,   20,  60,  and 

40,  respectively. 
1  m.  21.99  sec. 
-''7  ;    farm  worth,  $9- 
~  342. 
H,  $2568.58-1-  G,  $1- 

653.91  + 
Oct.  20. 
$640. 
2  h.  14  ra.  21  s.  A.  M. 


160 

1 

(( 

2 

11 

3 

ii 

4 

a 

5 

li 

6 

u 

7 

161 

8 

it 

9 

li 

10 

li 

11 

(; 

12 

(( 

13 

u 

14 

4( 

15 

162 

16 

u 

17 

u 

18 

p. 
162 


a 

163 


164 


165 


Ex. 

19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

31 
32 

33 
34 
35 
36 

37 
38 
39 

40 
41 


Answer. 

$133.57  + 
156  rd. 
$556  23. 

$105.80. 
122^  ft. 
lU  d. 
$12.66. 

48  miles. 

4338350  m50943|  in. 

$938,661 

10.59^^.  ^ 

Bal.,  $498  ;  due  June 

22,  1860. 
Aug.  28,  1859. 
A, $2400;  B,$3000; 

C,  $3375. 
$47.86- 
20  da. 
$640.50. 
6866.29  + ft. 
6  yd. 

$296.78- 

12^^  premium  on  Lon- 
don. 
50  ]b.  of  each. 
A,  $466| ;  B,  $833i ; 

C's  flour,  $10  per 

bbl. 
Length,  54  rd. ; 

breadth,  18  rd. 
19. 
Oldest,  $3909.79^ 

2d,  $8240.30. 
Youngest,  $2849.91. 


>i  more 


Farmer  gams; 

38  da. 

Base,  12  A.  3  R.  1126 

sq.  ft. 
Side,  218014.91sq. 

ft. 

Cubic  ft.,  83477400. 
$386.67. 
3  rd.  8  ft. 


ANSWERS. 

209 

Ex.  1                  Answer. 

p.     1  Ex. 

Answeb. 

50 

£7438  14s.  9d. 

169 

82 

3015.936  lb. 

51 

82000. 

(; 

83 

12300. 

52 

13  A.  1  R.  1.763  +  P. 

U 

84 

4^  ft. 

53 

.!!.026  on  a  dollar. 

a 

85 

823415. 

54 

5040. 

a 

86 

81154.99-. 

55 

2500. 

170 

87 

75  cents  and  95  cents 

56 

3  ft.  8.1429  + in. 

per  pound. 

57 

156. 

a 

88 

8173.93  +  . 

58 

152.05— acres. 

u 

89 

-^•4640.88-. 

59 

75,^. 

(( 

90 

86000  of  bank  stock. 

60 

82218876.10. 

u 

91 

1st  quality,  92  bbl. ; 

61 

S25512.40. 

2d,  54  bbl. ;    3d, 

62 

$236/3. 

54  bbl. 

63 

650  balls. 

C( 

92 

8  ft. 

64 

1  lb.  at  8 ;    8i  lb.  at 

« 

93 

82240. 

13;  8  1b.  at^l4. 

(( 

94 

19494.5  + lb. 

65 

84.467- 

u 

95 

M,  872.911 ; 

GQ 

From     top    to     top, 

N,  8102.08|. 

122.57  + ft.;    from 

171 

98 

8534.75. 

top      to      bottom, 

u 

97 

Twice  as  large. 

153.05  +  ft.,     and 

a 

98 

8.77. 

138.92  + ft. 

ii 

99 

85450000. 

67 

4  h.  30  min.  P.  M. 

u 

100 

A's,8108;  B's,8162. 

68 

E,    13    miles;  F,    21 
miles ;  G,  32  miles ; 

u 

101 

2400  bu.  at  80  cents 
a  bu. 

all  together,  in  8  h. 

(( 

102 

m- 

48  min. 

(( 

103 

AujT.  18. 

69 

3.568 +rd. 

172 

104 

A's;  89574^  ;    B's, 

70 

83365.94+ 

863881  ;^C's, 

71 

84095. 

8125375V- 

72 

5  calves,  5  lambs,  30 

u 

105 

6  in. 

kids. 

u 

106 

Gi.fo. 

73 

81029.13- 

u 

107 

25  ft. 

74 

10  in. 

u 

108 

12. 

75 

32^  lb.  at  14  and  16 

u 

109 

8364^9 

cents,  97i  lb.  at  12 

ii 

110 

210. 

and  18  cents. 

u 

111 

56  gal.  at  83.25 ;  20 

76 

A,  82640  ;   B,  82400. 

gal.  nt  81.80. 

77 

141.79  +  rd. 

a 

112 

81760.10. 

78 

6  ft. 

173 

113 

15  A.  2  R.  1076  sq. 

79 

X,  83915;  Y,  83045. 

vd. 

80  49A  mi.                          1 

(( 

114 

876000. 

81 

4t\  lb.                         1 

'ZiL 

) 

ANSWERS 

p. 

Ex. 

Answer. 

p. 

Ex 

1                Answebl 

173 

115 

A's,  $16277.21  ; 

177 

148 19801  rd. 

B's,  $3341.87; 

(; 

149 

15  days. 

C's,  $2880.92. 

li 

150 

|792  sq.ft. 

u 

116 

48i  da. 

a 

151 

m%' 

(( 

117 

$1.52J.- 

a 

152 

$30000. 

(( 

118 

28  1b. 

a 

153 

1  $29082.62-. 

u 

119 

288030  mi. 

a 

154 

j  17i|  oz. 

t( 

120 

$25200. 

a 

155 

$173103094564.40. 

174 

121 

^i\i%  dis. 

a 

156 

$.70  on  a  dollar. 

(( 

122 

$22.50. 

A,  $2800  ;B,  $3500; 

u 

123 

$68.36. 

C,  $4900. 

(( 

124 

169.26-. 

178 

157 

16.06  +  . 

tl 

125 

A's,  42  ;  B's,  21. 

(( 

158 

Sfo. 

(( 

126 

$660. 

a 

159 

$2191.21-. 

u 

127 

10,  20,  40,  80,  160, 

(( 

160 

734.65-. 

320,  640. 

(( 

161 

$2735.83-. 

(( 

128 

$12156.30. 

a 

162 

$63400. 

(( 

129 

$206.88- 

a 

163 

Fore-wheels,  97959.- 

11 

130 

221  rd.,  17  rd. 

495;  hind-wheels. 

175 

131 

25bu.  at  $1.75;   25 

12180.681  times. 

bu.  at  $1.80;  40 

a 

164 

188.2304  sq.  in. 

bu.  at  $2. 

179 

165 

$669.92.-. 

fC 

132 

$865.78. 

a 

166 

$16000. 

(( 

133 

10  min.  29y\3^  sec. 

a 

167 

$4000/3j. 

after  one. 

li 

168 

Falls  24  ft.,  bounds 

(( 

134 

$19757.863. 

12  ft. 

u 

135 

$6.17  +  . 

a 

169 

$1000. 

u 

136 

Net    proceeds,    $9- 

ii 

170 

$870. 

489.48;  due  May 

a 

171 

$855. 

20,  1860. 

li 

172 

8  ft.  4+in. 

176 

137 

2931  ft. 

ii 

173 

1020. 

ii 

138 

$5.87-. 

11 

174 

$68.36-. 

n 

139 

Elder,  $3030.36 ; 
younger,  $2525.30. 

180 

175 

H's,  $5250. 
J's,  $17250. 

li 

140 

$500. 

li 

176 

$72. 

li 

141 

25,^. 

li 

177 

8  days. 

li 

142 

1   at   $4;   5  at  $6; 

2  at  $8. 

a 

178 

2100  lb.  at  21|   c. 

per  lb. 

(( 

143 

8.66 -h  ft. 

(( 

179 

1331000. 

(( 

144 

$650. 

a 

180 

48f7/. 

u 

145 

21  21  3,  31,  3f . 

li 

181 

Length,  63  rd. 

(( 

146 

10.8  tons. 

Breadth,  35  rd. 

C( 

147 

$143.64. 

a 

182 

174^;t 

ANSWERS 

. 

211 

p. 

Ex. 

Answbb. 

p.     !  Ex 

Answeb. 

180 

183 

31.416  sq.  rd. 

1841214 

180  ft. 

<( 

184 

'^\l%' 

(C 

215 

$3693.77-. 

(( 

185 

104|f|sq.yd. 

a 

216 

41  da.  from  Oct.  1, 

181 

186 

Price  per  bu.$1.96y% 

or  Nov.  11. 

Gain  ^,22.85  +  . 

li 

217 

50000  lb. 

(( 

187 

65  1b. 

11 

218 

A's  money,  $750. 

u 

188 

$1000. 

B's       "       $1250. 

li 

189 

55 1  min. 

11 

219 

Wife,  $25000;    son. 

<( 

190 

£173  3s.  7.368d. 

$20000  ;        elder 

il 

191 

36.38 -ft. 

daughter,  $10000; 

li 

192 

1st,    $220.80;     2d, 
$331.20;     3d, 

younger  daughter, 
$5000. 

$496.80. 

185 

220 

5  A.  3  R.  7.68  P. 

(( 

193 

A,  $4150 ; 
W,  $14155. 

(( 

221 

Father,    32    years ; 
son,  10  years. 

182 

194 

1734  sq.  ft. 

(( 

222 

180.9 +  .  ft. 

n 

195 

8101449  +  . 

(( 

223 

8i  ft. 

(( 

196 

500  bags. 

u 

224 

17  cents  per  lb. 

<( 

197 

$26925. 

ii 

225 

816. 

ii 

198 

$1074.50. 

;( 

226 

$1841.20. 

ii 

199 

30.37-^. 

a 

227 

1t!-^  premium. 

li 

200 

$10407.106+. 

a 

228 

30  men,   5  women, 

ii 

201 

1  pt.  3.251  gills. 

and  20  boys. 

ii 

202 

$3910.94-. 

186 

229 

$720. 

il 

203 

Oats,  180  bu. ;  corn. 

ii 

230 

$629,426. 

140  bu. ;   barley. 

li 

231 

24  ft. 

140  bu. 

ii 

232 

$67.66. 

83 

204 

$629,426. 

*i 

233 

$1226.994,  at  7^. 

a 

205 

$4800. 

$1 174.789  at  6, ^,C.  I. 

u 

206 

$90. 

(I 

234 

521. 

u 

207 

$58. 

u 

235 

He"  traveled  650  mi. 

(( 

208 

$325.03. 

<; 

236 

ihh- 

(( 

209 

13    ft.    long;     336 
rails. 

u 

237 

12  yd.,  at  $1|;    16 
yd.,  at  $|. 

(( 

210 

128  in  rank,  32  in 
file. 

187 

238 

Eldest,  $7057.11; 
Second  son,  $6633.- 

84 

211 

Annuity,  $1065.85 ; 
owned     farm,     7 

68  ;    voungest, 
$6309.21. 

years. 

(( 

239; 

$9142.857. 

212 

9,  15,  and  21. 

u 

240 

15^. 

(( 

213 

$32500. 

(( 

241 

56  men. 

u 

242 

12,  15,  18,  21,  &  24 
men,  respectively. 

212 


p. 

Ex.  1 

187 

243 

u 

244 

u 

245 

188 

246 

a 

247 

u 

248 

ANSWERS 

AN8"VrBE. 

P. 

Ex. 

Answeb. 

$319.10-. 

188 

249 

$5. 

82.16. 

u 

250 

B's  stock,  $1600; 

3863080. 

C's  time,  15  mo 

Dec.  16,  1862. 

u 

251 

A's,  $960 ;   B's,  $ 

41  i  lb.  at  4  cents; 

600 ;  C's,  1640. 

41  lb.  at  5  cents, 

a 

252 

Same  as  in  251. 

and  1  lb.  at  9  cts. 

u 

253 

14001.042. 

17|,33t,48i,&63|. 

ROBINSON'S 

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Illinois,  Wisconsin,  Iowa,  and  throughout  the  Canadas. 

It  has  been  officially  recommended  by  the  proper  authorities,  for  use  in 
the  Schools  of  Indiana,  Minnesota,  and  Nebraska. 


Progressive  Table-Book.  This  is  a  beautifully  illustrated 

little  book,  on  the  plan  of  Object  Teaching. 

Progressive  Primary  Arithmetic,  illustrated.    Designed 

as  an  introduction  to  the  "  Intellectual  -tlrithmetic." 

Progressive  Intellectiial  Arithmetic,  on  the  inductite 

PLAN,  and  one  of  the  most  complete,  comprehensive,  and  disciplinary 
works  of  the  kind  ever  given  to  the  public. 

Rudiments  of  Written  Arithmetic,  for  graded  Schools, 

containing  copious  Slate  and  Blackboard  Exercises  for  beginners,  and  is 
designed  for  Graded  Schools. 

Progressive  Practical  Arithmetic,  containing  the  Theory 

of  Numbers,  in  connection  with  concise  Analytic  and  Synthetic  Methods 
of  Solution,  and  designed  as  a  complete  text-book  on  this  science,  for 
Common  Schools  and  Academies. 

It  has  not  been  encumbered  with  a  multiplicity  of  "  Notes,"  "  Suggestions,'* 
and  superfluous  operations  so  common  to  Practical  Arithmetics  of  the  present 
day,  and  which  prevent  the  cultivation  of  self-reliance,  clearness  of  thought,  and 
vigor  of  intellect. 


2 


Progressive  Higher  Arithmetic:  combining  the  Analytic 

and  Synthetic  Methods,  and  forming  a  complete  Treatise  on  Arith- 
metical Science,  in  all  its  Commercial  and  Business  Applications,  for 
Schools,  Academies  and  Commercial  Colleges. 

Particular  attention  has  been  given  to  the  preparation  of  *hose  subjects, 
which  are  absolutely  essential  to  make  good  accounta7iU  and  commercial 
business  men ;  and  among  them,  Percentage,  in  its  numerous  applications  to 
Stock-Jobbing,  Brokerage,  Insurance,  Banking,  Averaging  Accounts  Current, 
Interest  Accounts,  Domestic  and  Foreign  Exchange,  etc. 


Arithmetical  Examples.  This  book  has  recently  been  added 
to  the  Series,  and  contains  over  1,500  Practical  Examples,  promis- 
cnously  arranged,  and  without  the  answers  given,  involving  nearly  all 
the  principles  and  ordinary  processes  of  common  arithmetic,  designed 
thoroughly  to  test  the  pupil's  judgment;  to  cultivate  habits  of  patient 
investigation  and  self-reliance  ;  to  test  the  truth  and  accuracy  of  his 
own  processes  by  proof;  in  a  word,  to  make  him  independent  of  a 
text-book,  and  written  rules  and  analyses. 

The  most  noticeable  feature  of  this  work  will  be,  the  practical  character  of 
the  examples,  and  the  large  amount  of  facts,  statistics  and  information  of  recent 
date,  which  are  combined,  and  form  the  data  in  a  large  proportion  of  these  ex- 
amples. 

This  work  is  not  designed  for  beginners,  but  for  those  who  have"  acquired  at 
least  a  partial  knowledge  of  the  theory  and  applications  of  numbers  from  some 
other  work,  and  it  may  be  used  in  connection  with  any  other  book,  or  series  of 
books  on  this  subject,  for  Keview  or  Drill  Exercises. 

An  Edition  is  printed  exclusively  for  teacJiers,  containing  the  answers  at  the 
close  of  the  book. 


New  Elementary  Algebra  :  a  clear  and  practical  Treatise 
adapted  to  the  comprehension  of  beginners  in  the  Science. 

University  Algebra,  This  is  the  first  book  the  author  published 
on  this  subject,  in  1847,  although  subsequently  enlarged  and  twice 
revised.  No  book  of  the  kind  has  ever  been  so  favorably  received  and 
so  enthusiastically  admired  as  this. 

There  is  no  real  necessity  for  this  book  in  the  Series,  of  which  it  forms  a 
part,  but  it  may  be  used  by  those  who  do  not  desire  to  take  so  extensive 
and  thoroughly  scientific  a  course  as  is  given  in  the  "New  University  Al- 
gebra." 


8 

New  University  Algebra,  containing  many  new  and  original 
Methods  and  Applications  both  of  Theory  and  Practice,  and  is  designed 
for  Colleges  and  High  Schools. 

This  book  is  not  a  revision,  but  a  newly  prepared  and  recently  published 
work,  thoroughly  scientific  and  practical  in  its  discussions  and  applications.  It 
is  a  book,  lilled  with  gems,  and  most  of  them  original  with  the  author. 

New  G-eometry  and  Trigonometry,  embracing  Plane  and 

Solid  Geometry,  and  Plane  and  Spherical  Trigonometry,  with  numerous 
practical  Problems,  the  whole  newly  illustrated. 

New  Surveying  and  Navigation,  With  use  of  Instru- 
ments, essential  Elements  of  Trigonometry,  Mensuration,  and  the  ne- 
cessary Tables,  for  Schools,  Colleges,  and  Practical  Surveyors. 

This  work  is  not  a  revision,  but  an  entirely  new  tueatise,  finely  illustrated, 
full  and  complete,  with  numerous  examples,  embodying  the  most  modern  and 
practical  methods. 

Conic  Sections  and  Analytical  Geometry ;  recently 

prepared  for  High  Schools  and  Colleges. 

Differential  and  Integral  Calcnlns.    Re-written  and  en- 

larged;  finely  illustrated  ;  in  one  volume,  will  be  ready  April,  I860, 

Elementary  Astronomy.  An  Elementary  Class-book,  in 
which  mathematical  demonstrations  are  omitted. 

University  Astronomy.  Descriptive,  Theoretical  and  Phys- 
ical, designed  for  Schools,  Academies  and  Colleges.     Large  8vo, 

Concise  Mathematical  Operations.    Being  a  Sequel  to 

the  author's  Class-books,  with  much  addi:ional  matter. 


Key    to    Geometry   &    Trigonometry,    Analytical 
Geometry    &     Conic     Sections,     Surveying    & 

Navigation.      "With  some  additional  Astronomical  Problems,  in 
one  volume. 

Keys  to  the  Arithmetics  and  Algebras,  are  published 

for  the  use  of  Teachers. 


ROBINSON'S  COURSE  OF  MATHEMATICS 

in  whole  or  in  part,  are  used  in  the  State  Normal  Schools  of  New  Jersey, 
Pennsylvania,    Ohio,   Indiana,    Michigan,   Wisconsin,    Minnesota, 
Iowa,  Connecticut,  Massachusetts,  and  in  hundreds  of  the  best  Acad- 
emies and  High  Schools  of  these  and  the  other  States. 
The  "BROTHERS  OF  THE  CHRISTIAN  SCHOOLS"  have  ordered 

such  of  Robinson's  Mathematical  Series  as  are  adapted 

to  their  classes,  and  they  are  now  in  use  in  schools  under  their  supervision 
in  Montreal,  C.  W.,  Quebec,  C.  K,  Santa  Fe,  New  Mexico,  New  Orleans, 
St.  Louis,  Chicago,  Detroit,  Baltimore,  PhiladeljiMa,  New  York  City, 
Brooklyn,  Albany,  Troy,  Utica,  Rochester,  and  many  other  large  towns. 

ROBINSON'S  SERIES,  in  whole  or  in  part,  has  been 
adopted,  and  is  now  in  use  in  the  Public  Schools  of  New  York  City, 
Troy,  Utica,  Auburn,  Rochester,  Detroit,  Grand  Rapids,  Adrian, 
Kalamazoo,  Ann  Arbor,  Chicago,  Alton,  Joliett,  Milwaukie,  Madi- 
son, Janesville,  Ft.  Wayne,  Toledo,  Erie,  Pittsburgh,  Lexington, 
Louisville,  Springfield,  Hartford,  Middletown,  Bridgeport,  Provi- 
dence, and  hundreds  of  other  large  towns  in  all  the  States. 

EOBINSOH'S  HIGHER  MATHEMATICS  are  used,  wholly 
or  in  part,  in  Haiiiiltoii  College,  University  of  Rochester,  St.  Lawrence 
University,  Williams  College,  Amherst  College,  Tufts  College,  Elmira 
Female  College,  Ingham  University,  Dickenson  College,  St.  Vincent's 
College,  Manhattanville  College,  Pittsburgh  Female  College,  University 
of  St.  Mary  of  the  Lake,  University  of  Notre  Dame,  De  La  Salle  Institute, 
Alfred  University,  Ilavcrford  College,  Iron  City  Commercial  College, 
Middlebury  College,  Waterville  College,  Farmers'  College,  ilsbury  Female 
College,  Indiana  State  University,  Lind  University,  University  of  Chi- 
cago, Grinnell  College,  Lombard  University,  Fulton  Military  College, 
Olivet  College,  Adrian  College,  Kalamazoo  College,  State  Agricultural  Col- 
lege, Carroll  College,  VVesleyan  University,  Hillsdale  College,  Albion 
College,  Oberlin  College,  Iowa  Wesleyan  University,  Hamline  University, 
Baker  University,    Blue  Mount  Central  College,    Lawrence  University, 

and  in  many  others. 

1^  Single  Copies  of  such  books  of  Robinson's  Series  as  are  used  as 
Class-books,  will  be  furnished  to  Teachers,  and  School  Committees,  by 
mail  for  examination,  or  a  first  supply  for  introduction  by  express,  at  one- 
half  the  retail  price. 

|^°  The  "  Keys"  and  "  Mathematical  Operations"  will  bo  sent 
by  mail  on  receipt  of  the  full  retail  price,  or  by  express  at  expense  of  the 
party  ordering,  at  a  discount  of  25  per  cent  from  those  prices. 


# 


P  U  B  LI  S  TI  r  D     BY 


IVISON,  PHINNET,  BLAKEMAN  &  CO., 

48   &  50    WALKER   STREET,    N.   Y. 


ROBINSON'S    MATHEMATICAL    SERIES 

PROGRESSIVE  TABLE-BGOK 

PROGRESSIVE  PRIMARY  ARITUMETIC,  -        -        - 

PROGRESSIVE  INTELLECTUAL  ARITHMETIC,  - 
RUDIMENTS   OF  WRITTEN   ARITHMETIC,         -        - 
PROGRESSIVE  PRACTICAL    ARITHMETIC,         •        -        - 
KE7  TO   PRACTICAL   ARITHMETIC,    .        -        -        -        - 
PROGRESSIVE    HIGHER    ARITHMETIC,    .        -        -        - 
KEY   TO  PROGRESSIVE  HIGHER  ARITHMETIC,      -        - 

ARITHMETICAL    EXAMPLES, 

NEW  ELEMENTARY  ALGEBRA, - 

KEY  TO  NEW  ELEMENTARY  ALGEBRA,        -        -        - 

UNIVERSITY  ALlEBRA,  -        -' 

KEY  TO    UNIVEli^^TY  ALGEBRA,     .        .        -        -        - 

NEW  UNIVERSITY  ALGEBRA, 

KEY   TO  NEW    Ui\l\ERSITY  ALGEBRA,  - 
NEW  GEOMETRY  ANL    TRIGONOMETRY,    -        .        «        - 
NEW  SURVEYING   AND  NAVIGATION,    -        -        -        - 
ANALYTICAL    GEOMETRY  AND    CONIC  SECTIONS, 
DIFFERENTIAL  AND  INTEGRAL  CALCULUS,  -      (in  press) 

ELEMENTARY  ASTRONOMY, 

UNIVERSITY  ASTRONOMY '        " 

CONCISE  MATHEMATICAL     WPRATIONS - 
KEY  TO  GEOMETRY  &  TRIGONOMETRY,  CONIC  SECTIONS 
&  ANALYTICAL   GEOMETRY,  AND  SURVEYING,-        - 


^^^  The  most  liberal  terms  for  first  sujyplies,  for  in 
p  troduction,  and  specimen  co)yies,  for  " 

'CW  tlon.     Descriptive  Catalogues  gratis 


tion. 


""or  examina-^     % 


